diff --git a/Dockerfile b/Dockerfile
index b769346..317d9a4 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -5,7 +5,16 @@
 FROM golangci/golangci-lint:v2.14.0@sha256:ad862ba6b3798cbe0fd9fd7408d498fd74fbd2623a92406b2fd3898faf0bf98f AS lint
 WORKDIR /src
 COPY go.mod go.sum ./
-RUN go mod download
+# Without the time limit a stalled connection to the module proxy holds
+# this step, and every build on the host sharing it, until the kernel
+# drops the connection, which can take an hour. The download normally
+# takes under half a minute.
+RUN for attempt in 1 2 3; do \
+        timeout 180 go mod download && exit 0; \
+        echo "go mod download attempt $attempt failed or ran over 180s" >&2; \
+    done; \
+    echo "module download failed: giving up after 3 attempts" >&2; \
+    exit 1
 COPY . .
 # `golangci-lint run` silently ignores an unknown top-level key in
 # .golangci.yml, such as a misspelt `linters:`; `config verify` fails on it.
@@ -18,7 +27,13 @@ RUN golangci-lint run --config .golangci.yml ./...
 FROM golang:1.26.1@sha256:cd78d88e00afadbedd272f977d375a6247455f3a4b1178f8ae8bbcb201743a8a AS test
 WORKDIR /src
 COPY go.mod go.sum ./
-RUN go mod download
+# Limited and retried as in the lint phase above.
+RUN for attempt in 1 2 3; do \
+        timeout 180 go mod download && exit 0; \
+        echo "go mod download attempt $attempt failed or ran over 180s" >&2; \
+    done; \
+    echo "module download failed: giving up after 3 attempts" >&2; \
+    exit 1
 COPY . .
 RUN go test -timeout 90s -race -cover ./... || \
     { echo "--- Rerunning with -v for details ---"; \
@@ -36,7 +51,13 @@ RUN apk add --no-cache git
 RUN git config --system --add safe.directory /src
 WORKDIR /src
 COPY go.mod go.sum ./
-RUN go mod download
+# Limited and retried as in the lint phase above.
+RUN for attempt in 1 2 3; do \
+        timeout 180 go mod download && exit 0; \
+        echo "go mod download attempt $attempt failed or ran over 180s" >&2; \
+    done; \
+    echo "module download failed: giving up after 3 attempts" >&2; \
+    exit 1
 COPY . .
 
 # The VERSION build arg when one is given, otherwise
diff --git a/cmd/vaultik/dockermoddownload_test.go b/cmd/vaultik/dockermoddownload_test.go
new file mode 100644
index 0000000..5514a94
--- /dev/null
+++ b/cmd/vaultik/dockermoddownload_test.go
@@ -0,0 +1,42 @@
+package main_test
+
+import (
+	"strings"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+// TestDockerfileBoundsEveryModuleDownload fails unless every
+// `go mod download` in the Dockerfile runs under a time limit, is tried
+// a fixed number of times, and then fails the build with a message that
+// names the module download (issue #351). Like the version tests, this
+// parses the Dockerfile; that a stalled download really is cut off and
+// retried was checked by hand.
+func TestDockerfileBoundsEveryModuleDownload(t *testing.T) {
+	t.Parallel()
+
+	var downloads []string
+
+	for _, instruction := range instructions(t, productDockerfile) {
+		if strings.Contains(instruction, "go mod download") {
+			downloads = append(downloads, instruction)
+		}
+	}
+
+	require.NotEmpty(t, downloads, "%s must download modules",
+		productDockerfile)
+
+	for _, download := range downloads {
+		assert.Contains(t, download, "timeout 180 go mod download",
+			"%s: a module download must have a time limit: %s",
+			productDockerfile, download)
+		assert.Contains(t, download, "for attempt in 1 2 3",
+			"%s: a module download must be retried: %s",
+			productDockerfile, download)
+		assert.Contains(t, download, "module download failed",
+			"%s: a module download that never succeeds must say so: %s",
+			productDockerfile, download)
+	}
+}