Outlook Imap only syncs after Download Headers button is pressed

I have an endpoint running Outlook 2013 connected to Google Apps via Imap. The Imap snycing does not work unless we manually download the headers with the download headers icon. The syncing looks like it completes in Outlook but nothing new comes in. After the download headers button is pressed stuff flows in like normal until Outlook is restarted and then the button needs to be pressed again. It doesn't seem to matter how many messages are waiting to sync, it could be 20 or 2, nothing downloads without the button being pressed first. We have tried recreating the Outlook profile and resnycing the data as well as running a repair on Outlook itself.  

Unless we can figure something else we are going to try blowing Outlook away completely and reinstalling fresh. This user is very sensitive to changes, so we are trying to avoid that if possible.