This is really frustrating. Suddenly my IMAP account won't synchronize properly in Outlook 2013 (via Office 365) on Win 7. This account was working just fine for years and suddenly stopped working. I have deleted the entire account and folder set numerous times and tried different ways to make it work, but it still won't allow me to delete any emails in either the inbox or sent mail folders, nor will it automatically store sent mail in the sent items folder. The sync failures show up in the log. The exact same account works fine with Outlook 2011 on the Mac and Outlook 2013 on Win RT 8.1. More surprising, this does not affect all IMAP accounts. My Gmail still seems OK, as does another IMAP account.
What's up Microsoft? Is this a new bug you just introduced? This is pretty basic stuff. I hope you have an answer or will figure this out quickly. It affects a lot of people!