Restarting the entire server seems like overkill to me: restarting the mailserver by itself should be enough already. Something like: /etc/init.d/dovecot restart (this is for Fedora and Dovecot, may be different for other distros or mail server applications).
As a matter of fact, IMAP connections are usually dropped after a certain amount of time. Reconnecting will establish the connection again.
In your case I'm not even sure that the mail server causes the problem. Coul also be something on the Windows box (assuming that you don't run Outlook Express on Linux with some emulation).
Check the mail server log files for anomalies. Until that install a cron job to restart the mail server hourly.