Use persistent_login plugin's "Auth Token" support for Roundcube. The old way was very insecure and is subject to dictionary attack of the unsalted encrypted password stored in a browser cookie.

conf/persistent_login-sqlite.sql

@@ -0,0 +1,14 @@
+PRAGMA foreign_keys = ON;
+
+CREATE TABLE IF NOT EXISTS `auth_tokens` (
+    `token` TEXT NOT NULL,
+    `expires` TEXT NOT NULL,
+    `user_id` INTEGER NOT NULL,
+    `user_name` TEXT NOT NULL,
+    `user_pass` TEXT NOT NULL,
+    `host` TEXT NOT NULL,
+    PRIMARY KEY(`token`),
+    FOREIGN KEY(`user_id`) REFERENCES `users`(`user_id`) ON DELETE CASCADE
+);
+
+CREATE INDEX IF NOT EXISTS `user_id_fk_auth_tokens` ON `auth_tokens`(`user_id`);