diff --git a/.gitea/workflows/e2e.yml b/.gitea/workflows/e2e.yml
index 448040d..30fc7d3 100644
--- a/.gitea/workflows/e2e.yml
+++ b/.gitea/workflows/e2e.yml
@@ -35,10 +35,10 @@ on: [push]
 jobs:
     e2e-chrome:
         runs-on: ubuntu-latest
-        # Bounds the image build, a cold cache included, and both Chrome
+        # Bounds the image build, a cold cache included, and the three Chrome
         # programs, so a hung browser frees the shared runner. README.md
         # "In CI" has the measured times.
-        timeout-minutes: 20
+        timeout-minutes: 40
         steps:
             # actions/checkout v4.2.2, 2026-02-22
             - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683
diff --git a/README.md b/README.md
index d08f843..4de8451 100644
--- a/README.md
+++ b/README.md
@@ -542,6 +542,29 @@ one profile yields a single extension id, not two: Chrome does not load a second
 copy of an id it already has. The assertions are annotated as observations, so a
 Chrome that ever changes this fails the run instead of passing it.
 
+Last, `make test-e2e` runs `tests/e2e/slowApproval.js`, which leaves a
+transaction approval and a signature approval open for seven minutes with both
+windows minimized, then restores and approves both and requires the site to
+receive the hash of the transaction the stub node received and a signature that
+recovers to the address. Before the background worker kept itself running while
+an approval is pending, Chrome stopped it about six minutes in and neither
+request was ever answered
+([#540](https://git.eeqj.de/sneak/AutistMask/issues/540)). The windows are
+minimized through the DevTools protocol (`Browser.setWindowBounds`), and the run
+fails unless both pages then report themselves hidden: Chrome slows a hidden
+page's timers to once a minute, so anything the window did to keep the worker
+running would fail here. It is its own program and does not use Playwright:
+Playwright keeps DevTools attached to the background worker, and Chrome never
+stops a worker DevTools is attached to, so no wait in the suite above can show
+the worker stopping. It starts Chromium itself, speaks the DevTools protocol
+over `--remote-debugging-pipe`, and attaches to pages only. Before raising the
+approvals it requires the worker to stop on its own with nothing pending, so a
+run in which something else keeps the worker running fails. The site is
+connected and the RPC endpoint set through the extension's own screens, against
+the Firefox suite's loopback dApp page and stub node
+(`tests/e2e/firefox/dapp.js`). Unlike the suite above, it does not fail on page
+errors.
+
 ### Firefox (`make test-e2e-firefox`)
 
 `make test-e2e-firefox` builds `dist/firefox/` and drives the **real popup in a
@@ -722,11 +745,13 @@ installing Firefox, geckodriver and their system libraries. Both scripts now
 build their image with `--no-cache`, so every run pays the cold figure. Those
 `e2e-chrome` runs predate the cases that wait in real time for a receipt to end
 in error. `make test-e2e` took 3m51s locally with its image cached, so with the
-image rebuilt every run, an `e2e-chrome` run comes to about seven minutes.
+image rebuilt every run, an `e2e-chrome` run comes to about seven minutes. The
+approvals left open for seven minutes (`tests/e2e/slowApproval.js`) add about
+eight more, so about fifteen.
 
 Each e2e job has a `timeout-minutes` cap, so a hung build or browser ends the
 job instead of holding the shared runner: `e2e-firefox` 15 minutes and
-`e2e-chrome` 20, each over two and a half times the job's slowest cold run. A
+`e2e-chrome` 40, each over two and a half times the job's slowest cold run. A
 job that reaches its cap has hung; read it as a hang, not as a slow run to
 retry. The `check` job has no cap: `.gitea/workflows/check.yml` is the canonical
 copy from `sneak/prompts`, kept byte-identical.
@@ -821,6 +846,20 @@ on the next event. Two consequences shape every recurring job in the background:
   service worker at all — the one remaining user of it, `src/shared/ens.js`,
   runs only in the popup and is marked as such.
 
+Pending approvals are the exception: an approval waiting for the user, and the
+site's request waiting on it, live only in the worker's memory, and only the
+worker that received the request can answer it. Left alone, Chrome stopped the
+worker about six minutes after a site's request even with the approval window
+still open, and the user's answer then reached nobody. So the worker keeps
+itself running while any approval is pending: raising an approval starts a
+`setInterval` that calls `runtime.getPlatformInfo()` every 20 seconds, and
+Chrome counts each extension call as activity. The timer stops itself once
+nothing is pending, and the worker then stops as it otherwise would. The timer
+is the worker's own, so it does not depend on the approval window being visible;
+a timer in the window would, because Chrome slows a hidden page's timers to once
+a minute. A worker that stops for another reason, a crash say, still loses the
+approvals open in it.
+
 The job also carries a freshness guard, and a guard must never be timed to the
 alarm period it gates. The guard is measured from the moment the last run
 finished, which is one run-duration after the alarm that started it, so a guard
diff --git a/script/test-e2e b/script/test-e2e
index 2246905..4382bdd 100755
--- a/script/test-e2e
+++ b/script/test-e2e
@@ -97,6 +97,18 @@ main() {
         -e HOME=/tmp \
         "$(cat "$IIDFILE")" \
         node tests/e2e/storagePartition.js
+
+    # Approvals left open for seven minutes in minimized windows, past the
+    # point where Chrome stopped the background worker when nothing kept it
+    # running. Its own program, without Playwright: Playwright keeps DevTools
+    # attached to the worker, and Chrome never stops a worker DevTools is
+    # attached to. It reaches nothing but its own loopback server.
+    echo "Running the approvals left open for seven minutes..."
+    docker run --rm \
+        --ipc=host \
+        -e HOME=/tmp \
+        "$(cat "$IIDFILE")" \
+        node tests/e2e/slowApproval.js
 }
 
 main "$@"
diff --git a/src/background/index.js b/src/background/index.js
index 2b55689..5e0e7cc 100644
--- a/src/background/index.js
+++ b/src/background/index.js
@@ -44,6 +44,7 @@ const {
 
 const {
     actionApi,
+    getPlatformInfo,
     runtimeApi,
     tabsQuery,
     tabsSendMessage,
@@ -67,6 +68,29 @@ const connectedSites = {};
 // Pending approval requests: { id: { origin, resolve } }
 const pendingApprovals = {};
 
+// An approval, and the site's request waiting on it, exist only in this
+// worker's memory. Left alone, Chrome stopped the worker about six minutes
+// after the site's request while the user was still deciding, and the approval
+// was lost with it. Chrome counts an extension call as activity, so while any
+// approval is pending this worker makes one every 20 seconds, inside Chrome's
+// 30-second idle limit. Each function below that raises an approval starts the
+// timer, and it stops itself once nothing is pending. It is the worker's own
+// timer, so it runs whether or not the approval window is visible.
+let keepRunningTimer = null;
+
+function keepRunningWhileApprovalsPending() {
+    if (keepRunningTimer) return;
+    keepRunningTimer = setInterval(() => {
+        if (Object.keys(pendingApprovals).length === 0) {
+            clearInterval(keepRunningTimer);
+            keepRunningTimer = null;
+            return;
+        }
+        // Only the call matters; its answer is not used.
+        getPlatformInfo().catch(() => {});
+    }, 20000);
+}
+
 // One transaction approval at a time, wallet-wide.
 //
 // The transaction a site asks for is populated before its approval window
@@ -515,6 +539,7 @@ function requestApproval(origin) {
     return new Promise((resolve) => {
         const id = crypto.randomUUID();
         pendingApprovals[id] = { id, origin, resolve, type: "site" };
+        keepRunningWhileApprovalsPending();
 
         if (actionNs && typeof actionNs.openPopup === "function") {
             showInToolbarPopup(id);
@@ -566,6 +591,7 @@ function requestTxApproval(origin, approvedTx, approvedFrom, slot) {
             type: "tx",
         };
         if (slot) slot.approvalId = id;
+        keepRunningWhileApprovalsPending();
 
         openApprovalWindow(id);
     });
@@ -586,6 +612,7 @@ function requestSignApproval(origin, signParams, approvedFrom) {
             resolve,
             type: "sign",
         };
+        keepRunningWhileApprovalsPending();
 
         openApprovalWindow(id);
     });
@@ -606,6 +633,7 @@ function requestNetworkApproval(origin, currentNetworkId, requestedNetworkId) {
             resolve,
             type: "network",
         };
+        keepRunningWhileApprovalsPending();
 
         openApprovalWindow(id);
     });
diff --git a/src/shared/browserApi.js b/src/shared/browserApi.js
index c512286..8584528 100644
--- a/src/shared/browserApi.js
+++ b/src/shared/browserApi.js
@@ -145,6 +145,14 @@ function sendMessage(message) {
     return invoke(runtimeApi(), "sendMessage", message);
 }
 
+/**
+ * @returns {Promise<Object>} the operating system and processor the browser
+ *     runs on.
+ */
+function getPlatformInfo() {
+    return invoke(runtimeApi(), "getPlatformInfo");
+}
+
 /**
  * Send a message nobody is expected to answer, and swallow the fact that
  * nobody did.
@@ -262,6 +270,7 @@ module.exports = {
     actionApi,
     alarmsApi,
     extensionApi,
+    getPlatformInfo,
     hasBrowserNamespace,
     notify,
     runtimeApi,
diff --git a/tests/backgroundApproval.test.js b/tests/backgroundApproval.test.js
index 07218fd..f9e8697 100644
--- a/tests/backgroundApproval.test.js
+++ b/tests/backgroundApproval.test.js
@@ -264,6 +264,7 @@ function loadBackground(options) {
                     connectListener = fn;
                 },
             },
+            getPlatformInfo: jest.fn((cb) => cb({ os: "linux" })),
             lastError: null,
         },
         windows: {
@@ -878,6 +879,43 @@ describe("one transaction approval at a time", () => {
     });
 });
 
+// Chrome stops an idle worker, and the approvals in it go with it
+// (https://git.eeqj.de/sneak/AutistMask/issues/540). tests/e2e/slowApproval.js
+// shows the worker kept running in Chrome; this shows the calls stop once the
+// approval is answered, so the worker can stop again.
+describe("the worker keeps running while an approval is pending", () => {
+    test("an extension call every 20 seconds until the approval is answered", async () => {
+        const startTimer = jest
+            .spyOn(global, "setInterval")
+            .mockImplementation(() => 1);
+        const stopTimer = jest
+            .spyOn(global, "clearInterval")
+            .mockImplementation(() => {});
+        try {
+            const bg = loadBackground();
+            const calls = global.chrome.runtime.getPlatformInfo;
+            bg.requestTx();
+            await settle();
+            expect(startTimer).toHaveBeenCalledTimes(1);
+            expect(startTimer.mock.calls[0][1]).toBe(20000);
+            const tick = startTimer.mock.calls[0][0];
+
+            tick();
+            expect(calls).toHaveBeenCalledTimes(1);
+
+            // The user closes the approval window, which rejects it.
+            bg.closeWindow(1);
+            await settle();
+            tick();
+            expect(calls).toHaveBeenCalledTimes(1);
+            expect(stopTimer).toHaveBeenCalledWith(1);
+        } finally {
+            startTimer.mockRestore();
+            stopTimer.mockRestore();
+        }
+    });
+});
+
 // A page that asks again before the user has answered its last connection or
 // signature request is refused, instead of opening one more window per call.
 describe("one connection and one signature approval per site at a time", () => {
diff --git a/tests/e2e/slowApproval.js b/tests/e2e/slowApproval.js
new file mode 100644
index 0000000..936b792
--- /dev/null
+++ b/tests/e2e/slowApproval.js
@@ -0,0 +1,530 @@
+// A transaction approval and a signature approval the user leaves open for
+// seven minutes, their windows minimized, are still answered, and the site
+// receives both results (https://git.eeqj.de/sneak/AutistMask/issues/540).
+//
+// Both approvals, and the site's requests waiting on them, live only in the
+// background worker's memory. With nothing else going on, Chrome stopped that
+// worker about six minutes after the site's request, while the window was
+// still open, and the user's answer then reached nobody. While an approval is
+// pending, the worker now makes an extension call every 20 seconds, which
+// keeps it running (keepRunningWhileApprovalsPending() in
+// src/background/index.js). The windows are minimized for the wait because
+// Chrome slows a hidden page's timers to once a minute after a few minutes,
+// so anything the window itself did to keep the worker running would fail
+// here.
+//
+// A separate program from run.js, and not driven by Playwright: Playwright
+// keeps DevTools attached to the background worker, and Chrome never stops a
+// worker DevTools is attached to, so in run.js the worker outlives any wait
+// and a wait there proves nothing. This program starts Chromium itself and
+// speaks the DevTools protocol over the pipe Chromium opens for it
+// (--remote-debugging-pipe), attaching to pages only, never to the worker.
+// Before the approvals are raised it watches the worker stop on its own, so a
+// run in which something else keeps the worker running cannot pass.
+//
+// The dApp page and the stub node are the Firefox suite's loopback ones
+// (tests/e2e/firefox/dapp.js). The site is connected and the node chosen
+// through the extension's own screens, so nothing is written to its storage
+// from outside.
+//
+// Run through script/test-e2e, which builds the extension and the pinned
+// container.
+//
+//   node tests/e2e/slowApproval.js
+
+"use strict";
+
+const fs = require("fs");
+const os = require("os");
+const path = require("path");
+const { spawn } = require("child_process");
+
+const { chromium } = require("playwright-core");
+const {
+    Transaction,
+    getAddress,
+    getBytes,
+    hexlify,
+    parseEther,
+    toQuantity,
+    toUtf8Bytes,
+    verifyMessage,
+} = require("ethers");
+
+const { PASSWORD } = require("./harness");
+const { STUB_COUNTERPARTY } = require("./network");
+const { startDappServer } = require("./firefox/dapp");
+
+const DIST_CHROME = path.resolve(__dirname, "..", "..", "dist", "chrome");
+
+// Chrome stopped the worker six minutes after the site's request when nothing
+// kept it running, so the approvals are left open for longer than that.
+const APPROVAL_WAIT_MS = 7 * 60 * 1000;
+
+// With nothing pending, Chrome stops the worker 30 seconds after its last
+// event; this is how long the program waits to see that.
+const IDLE_STOP_TIMEOUT_MS = 90000;
+
+const SIGN_HEX = hexlify(toUtf8Bytes("AutistMask e2e: a slow signature"));
+
+const checks = [];
+let failed = 0;
+
+function check(name, cond, detail) {
+    checks.push(name);
+    if (cond) {
+        console.log("ok " + checks.length + " - " + name);
+    } else {
+        failed += 1;
+        console.log("not ok " + checks.length + " - " + name);
+        if (detail) console.log("  " + detail);
+    }
+}
+
+function sleep(ms) {
+    return new Promise((resolve) => setTimeout(resolve, ms));
+}
+
+// Poll `probe` until it returns something truthy, and return that.
+async function until(what, probe, timeout = 30000) {
+    const deadline = Date.now() + timeout;
+    for (;;) {
+        const value = await probe().catch(() => null);
+        if (value) return value;
+        if (Date.now() > deadline) {
+            throw new Error(
+                "gave up after " + timeout + "ms waiting for " + what,
+            );
+        }
+        await sleep(250);
+    }
+}
+
+// The DevTools protocol over Chromium's pipe: commands go to its fd 3, and
+// replies and events come back on its fd 4, each one JSON message ended by a
+// NUL byte. Events are not used and are dropped. Returns send(method, params,
+// sessionId), which resolves with the command's result.
+function devtools(browser) {
+    const waiting = new Map();
+    let nextId = 1;
+    let pending = "";
+    const replies = browser.stdio[4];
+    replies.setEncoding("utf8");
+    replies.on("data", (chunk) => {
+        pending += chunk;
+        let end;
+        while ((end = pending.indexOf("\0")) !== -1) {
+            const message = JSON.parse(pending.slice(0, end));
+            pending = pending.slice(end + 1);
+            const caller = waiting.get(message.id);
+            if (!caller) continue;
+            waiting.delete(message.id);
+            if (message.error) {
+                caller.reject(
+                    new Error(caller.method + ": " + message.error.message),
+                );
+            } else {
+                caller.resolve(message.result);
+            }
+        }
+    });
+    replies.on("close", () => {
+        for (const caller of waiting.values()) {
+            caller.reject(new Error("the browser exited"));
+        }
+        waiting.clear();
+    });
+    return (method, params = {}, sessionId) =>
+        new Promise((resolve, reject) => {
+            const id = nextId++;
+            waiting.set(id, { method, resolve, reject });
+            browser.stdio[3].write(
+                JSON.stringify({ id, method, params, sessionId }) + "\0",
+            );
+        });
+}
+
+// Attach to a page and return a function that evaluates an expression in it,
+// awaiting a promise it returns, and resolves with the value.
+async function attach(send, targetId) {
+    const { sessionId } = await send("Target.attachToTarget", {
+        targetId,
+        flatten: true,
+    });
+    return async (expression) => {
+        const r = await send(
+            "Runtime.evaluate",
+            { expression, awaitPromise: true, returnByValue: true },
+            sessionId,
+        );
+        if (r.exceptionDetails) {
+            throw new Error(
+                "evaluating " +
+                    expression.slice(0, 80) +
+                    " threw: " +
+                    JSON.stringify(r.exceptionDetails.exception || {}),
+            );
+        }
+        return r.result.value;
+    };
+}
+
+// Whether the page has loaded and shows the element with this id: the
+// `hidden` class showView() keeps on every other view is on neither it nor
+// anything around it.
+function shows(id) {
+    return (
+        "document.readyState === 'complete' &&" +
+        " !!document.getElementById(" +
+        JSON.stringify(id) +
+        ") && !document.getElementById(" +
+        JSON.stringify(id) +
+        ").closest('.hidden')"
+    );
+}
+
+// Set an input's value and fire the input event typing would fire.
+function typeInto(id, value) {
+    return (
+        "(() => { const el = document.getElementById(" +
+        JSON.stringify(id) +
+        "); el.value = " +
+        JSON.stringify(value) +
+        "; el.dispatchEvent(new Event('input', { bubbles: true })); })()"
+    );
+}
+
+function click(id) {
+    return "document.getElementById(" + JSON.stringify(id) + ").click()";
+}
+
+// The outcome of a request the dApp page started with __dapp.start(), or
+// {settled: "pending"} if it has not settled within `timeout`.
+function settled(key, timeout = 30000) {
+    return (
+        "Promise.race([window.__dapp.settle(" +
+        JSON.stringify(key) +
+        "), new Promise((r) => setTimeout(() => r({ settled: 'pending' }), " +
+        timeout +
+        "))])"
+    );
+}
+
+async function main() {
+    if (!fs.existsSync(path.join(DIST_CHROME, "manifest.json"))) {
+        console.error(
+            "slowApproval: no unpacked build at " +
+                DIST_CHROME +
+                " — run make build first",
+        );
+        process.exitCode = 1;
+        return;
+    }
+
+    const node = await startDappServer();
+    const profile = fs.mkdtempSync(
+        path.join(os.tmpdir(), "autistmask-slow-approval-"),
+    );
+    const browser = spawn(
+        chromium.executablePath(),
+        [
+            "--headless",
+            // The container runs unprivileged, as in harness.js.
+            "--no-sandbox",
+            "--remote-debugging-pipe",
+            "--user-data-dir=" + profile,
+            "--disable-extensions-except=" + DIST_CHROME,
+            "--load-extension=" + DIST_CHROME,
+            // Nothing but the loopback dApp page and stub node can be reached.
+            "--host-resolver-rules=MAP * ~NOTFOUND, EXCLUDE 127.0.0.1",
+            "about:blank",
+        ],
+        { stdio: ["ignore", "ignore", "ignore", "pipe", "pipe"] },
+    );
+
+    try {
+        const send = devtools(browser);
+        const targets = async () =>
+            (await send("Target.getTargets")).targetInfos;
+
+        const worker = await until("the background worker", async () =>
+            (await targets()).find(
+                (t) =>
+                    t.type === "service_worker" &&
+                    t.url.startsWith("chrome-extension://"),
+            ),
+        );
+        // The extension id is the host of the worker's URL, as in harness.js.
+        const popupUrl =
+            "chrome-extension://" +
+            new URL(worker.url).host +
+            "/src/popup/index.html";
+        const workerRunning = async () =>
+            (await targets()).some((t) => t.url === worker.url);
+        const openPage = async (url) => {
+            const { targetId } = await send("Target.createTarget", { url });
+            return { targetId, evaluate: await attach(send, targetId) };
+        };
+        const approvalPages = async () =>
+            (await targets()).filter(
+                (t) => t.type === "page" && t.url.includes("?approval="),
+            );
+
+        // A wallet, through the popup's own screens, and the stub node as its
+        // RPC endpoint, through Settings.
+        const popup = await openPage(popupUrl);
+        await until("the welcome screen", () =>
+            popup.evaluate(shows("view-welcome")),
+        );
+        await popup.evaluate(click("btn-welcome-add"));
+        await until("the add wallet screen", () =>
+            popup.evaluate(shows("view-add-wallet")),
+        );
+        await popup.evaluate(click("btn-generate-phrase"));
+        await until("a generated recovery phrase", () =>
+            popup.evaluate(
+                "document.getElementById('wallet-mnemonic').value.trim()" +
+                    ".split(/\\s+/).length >= 12",
+            ),
+        );
+        await popup.evaluate(typeInto("add-wallet-password", PASSWORD));
+        await popup.evaluate(typeInto("add-wallet-password-confirm", PASSWORD));
+        await popup.evaluate(click("btn-add-wallet-confirm"));
+        await until(
+            "the main screen",
+            () => popup.evaluate(shows("view-main")),
+            60000,
+        );
+        await popup.evaluate(click("btn-settings"));
+        await until("the settings screen", () =>
+            popup.evaluate(shows("view-settings")),
+        );
+        await popup.evaluate(typeInto("settings-rpc", node.rpcUrl));
+        await popup.evaluate(click("btn-save-rpc"));
+        await until("the stub node saved as the RPC endpoint", () =>
+            popup.evaluate(
+                "new Promise((resolve) => chrome.storage.local.get(" +
+                    "'autistmask', (r) => resolve(r.autistmask.rpcUrl === " +
+                    JSON.stringify(node.rpcUrl) +
+                    ")))",
+            ),
+        );
+        await send("Target.closeTarget", { targetId: popup.targetId });
+
+        // The site, connected through the real prompt with "Remember", so
+        // the connection is stored rather than held by the worker.
+        const dapp = await openPage(node.url);
+        await until("the injected provider", () =>
+            dapp.evaluate("!!window.ethereum && !!window.__dapp"),
+        );
+        await dapp.evaluate(
+            "window.__dapp.start('accounts', 'eth_requestAccounts', [])",
+        );
+        const prompt = await until(
+            "the connection prompt",
+            async () => (await approvalPages())[0],
+        );
+        const inPrompt = await attach(send, prompt.targetId);
+        await until("the connection prompt's screen", () =>
+            inPrompt(shows("view-approve-site")),
+        );
+        await inPrompt(
+            "document.getElementById('approve-remember').checked = true",
+        );
+        // The prompt closes itself on the click.
+        await inPrompt(click("btn-approve")).catch(() => {});
+        const accounts = await dapp.evaluate(settled("accounts"));
+        if (accounts.settled !== "resolved") {
+            throw new Error(
+                "the site could not be connected: " + JSON.stringify(accounts),
+            );
+        }
+        const address = getAddress(accounts.result[0]);
+        console.log("# address " + address + ", site " + node.origin);
+
+        // The control: with nothing pending, the worker stops on its own.
+        // Were something else keeping it running, the wait below would
+        // prove nothing.
+        const idleStart = Date.now();
+        const stoppedWhenIdle = await until(
+            "the idle worker to stop",
+            async () => !(await workerRunning()),
+            IDLE_STOP_TIMEOUT_MS,
+        ).catch(() => false);
+        check(
+            "with nothing pending, Chrome stops the background worker on its own",
+            stoppedWhenIdle,
+            "the worker was still running " +
+                IDLE_STOP_TIMEOUT_MS / 1000 +
+                "s after its last event, so something other than the " +
+                "approval windows is keeping it running",
+        );
+        console.log(
+            "# idle worker stopped after " +
+                Math.round((Date.now() - idleStart) / 1000) +
+                "s",
+        );
+
+        // A transaction approval and a signature approval, both open at once.
+        await dapp.evaluate(
+            "window.__dapp.start('tx', 'eth_sendTransaction', [" +
+                JSON.stringify({
+                    from: address,
+                    to: STUB_COUNTERPARTY,
+                    value: toQuantity(parseEther("0.01")),
+                }) +
+                "])",
+        );
+        await until("the transaction approval window", async () =>
+            (await approvalPages()).length === 1 ? true : null,
+        );
+        await dapp.evaluate(
+            "window.__dapp.start('sign', 'personal_sign', [" +
+                JSON.stringify(SIGN_HEX) +
+                ", " +
+                JSON.stringify(address) +
+                "])",
+        );
+        const windows = await until("both approval windows", async () => {
+            const pages = await approvalPages();
+            return pages.length === 2 ? pages : null;
+        });
+        let txWindow = null;
+        let signWindow = null;
+        const windowIds = [];
+        for (const page of windows) {
+            const evaluate = await attach(send, page.targetId);
+            const view = await until("an approval screen", () =>
+                evaluate(
+                    "(" +
+                        shows("view-approve-tx") +
+                        ") ? 'tx' : (" +
+                        shows("view-approve-sign") +
+                        ") ? 'sign' : null",
+                ),
+            );
+            if (view === "tx") txWindow = evaluate;
+            if (view === "sign") signWindow = evaluate;
+            const { windowId } = await send("Browser.getWindowForTarget", {
+                targetId: page.targetId,
+            });
+            windowIds.push(windowId);
+        }
+        if (!txWindow || !signWindow) {
+            throw new Error("the two windows are not one of each kind");
+        }
+        const setWindowState = (windowState) =>
+            Promise.all(
+                windowIds.map((windowId) =>
+                    send("Browser.setWindowBounds", {
+                        windowId,
+                        bounds: { windowState },
+                    }),
+                ),
+            );
+
+        // The user minimizes both windows while deciding.
+        await setWindowState("minimized");
+        const bothHidden = await until(
+            "both approval pages hidden",
+            async () =>
+                (await txWindow("document.visibilityState")) === "hidden" &&
+                (await signWindow("document.visibilityState")) === "hidden",
+        ).catch(() => false);
+        check(
+            "both approval windows are minimized, and their pages are hidden",
+            bothHidden,
+            "a page still reports itself visible, so the wait below would " +
+                "not show what happens to a minimized approval",
+        );
+
+        // The user takes seven minutes. The worker is checked every two
+        // seconds, and the wait ends early if Chrome stops it.
+        const opened = Date.now();
+        let stoppedAfter = null;
+        while (Date.now() - opened < APPROVAL_WAIT_MS) {
+            if (!(await workerRunning())) {
+                stoppedAfter = Math.round((Date.now() - opened) / 1000);
+                break;
+            }
+            await sleep(2000);
+        }
+        check(
+            "the background worker keeps running while both approvals wait in minimized windows",
+            stoppedAfter === null,
+            "Chrome stopped the worker " +
+                stoppedAfter +
+                "s after the approvals opened",
+        );
+
+        // Back on screen to be answered.
+        await setWindowState("normal");
+        await txWindow(typeInto("approve-tx-password", PASSWORD));
+        await txWindow(click("btn-approve-tx"));
+        await signWindow(typeInto("approve-sign-password", PASSWORD));
+        // The window closes itself once the signature is handed over.
+        await signWindow(click("btn-approve-sign")).catch(() => {});
+
+        const tx = await dapp.evaluate(settled("tx"));
+        const broadcast = node.broadcast.map((raw) => Transaction.from(raw));
+        check(
+            "the transaction approved after seven minutes reaches the site",
+            tx.settled === "resolved" &&
+                broadcast.length === 1 &&
+                tx.result === broadcast[0].hash &&
+                getAddress(broadcast[0].from) === address,
+            "the page got " +
+                JSON.stringify(tx) +
+                " and the node received " +
+                broadcast.length +
+                " transaction(s)",
+        );
+
+        const sign = await dapp.evaluate(settled("sign"));
+        check(
+            "the signature approved after seven minutes reaches the site",
+            sign.settled === "resolved" &&
+                getAddress(verifyMessage(getBytes(SIGN_HEX), sign.result)) ===
+                    address,
+            "the page got " + JSON.stringify(sign),
+        );
+    } catch (e) {
+        failed += 1;
+        console.log("# ERROR: " + (e && e.stack ? e.stack : e));
+    } finally {
+        if (browser.exitCode === null && browser.signalCode === null) {
+            const exited = new Promise((resolve) =>
+                browser.once("exit", resolve),
+            );
+            browser.kill();
+            await exited;
+        }
+        await node.close();
+        // Chromium's helper processes can still be writing to the profile
+        // for a moment after the browser process itself has exited.
+        fs.rmSync(profile, { recursive: true, force: true, maxRetries: 5 });
+    }
+
+    console.log("1.." + checks.length);
+    if (checks.length === 0) {
+        console.log("# FAILED: this program asserted nothing");
+        process.exitCode = 1;
+        return;
+    }
+    console.log(
+        "# " +
+            (checks.length - failed) +
+            "/" +
+            checks.length +
+            " checks passed",
+    );
+    if (failed > 0) {
+        console.log("# FAILED");
+        process.exitCode = 1;
+    }
+}
+
+main().catch((e) => {
+    console.error("slowApproval: " + (e && e.stack ? e.stack : e));
+    process.exitCode = 1;
+});