Mutt seems to sync to Gmail IMAP only on quit
Manual syncing
Try $:
$ sync-mailbox save changes to mailbox
Automatic syncing?
You can't make mutt
do that automatically/periodically, by design. The reasoning, as I understand it, is that it might lead to data loss. E.g., when you mark something as deleted, you'd normally be able to undo, and auto-syncing would interfere with that (see Re: Auto sync-mailbox - no way! and Mutt, IMAP and auto'refresh').
Mailboxes should be synced in any case when you change folders/mailboxes.
Alternatives
There's a source patch adding a timeout-hook to mutt you could use to periodically call sync-mailbox
, but it's for mutt 1.5.9
and I don't know if it can be applied against the current version.
You could also set up OfflineIMAP (or isync). It's designed for synchronizing local mailbox(es) with a central IMAP one. You can then use another notification system (like e.g. mutt
's built-in one or mail-notification
etc.) to watch your local box for changes.