This bug is the result of Outlook opening too many connections to the IMAP server. Gmail sets a limit to the number of connections that can be opened and Outlook wants more. This will be fixed in RTM. Until then, the best solution is to remove the account from the Send and Receive Settings as described below.
Outlook 2013 users discovered an annoying bug when they have a Gmail account configured to use IMAP: an IMAP error message keeps coming up, every few minutes (or less).
I put an end to the error by opening the Send and Receive settings dialog and deselecting the option to include the Gmail account in the Send and Receive. While the account doesn't update every time Outlook does an automated send and receive, the folder is synced when I open the folder to read mail. It takes a couple of seconds for Outlook to refresh the folder but dismissing the IMAP error dialogs takes much longer.
To change the setting, open the send and receive settings dialog using Ctrl+Alt+S. Select the send and receive account and click Edit. Select the gmail account on the left then deselect the option to include the gmail account in the send and receive.
Published August 14 2012