Hello,
I have a Win 7 Pro laptop running Office 365 Pro Plus, and Outlook 2013 is part of that package. For some reason, Outlook isn't syncing to the Exchange 365 server. Even though it says "Connected" at the bottom, and that "All Folders Are Up to Date", I'm still not getting a full sync. Example: I can delete a message from my inbox on my Win 7 computer, yet the message doesn't delete from the Outlook Web App, or my iPhone or iPad. Or, I can delete a message from my iPad or iPhone, and it will delete on Outlook Web App but not on my laptop running Outlook. In other words, my Win 7 PC running Outlook is the odd man out. My iOS devices and the Outlook Web App always seem to be in sync.
I did notice that at the bottom of the message list in my inbox in Outlook, there's a link telling me "there are more messages on the server". I click that link, and it takes a few seconds for my inbox messages to update. Once they do, I see messages I've already deleted before. This tends to improve the sync function as well, but only temporarily.
I did try to repair my profile by going to File --> Account Settings and then choosing Repair. That didn't really seem to change anything.
I also tried running a full Office 365 repair in Add/Remove Programs, but that didn't fix it either.
I have downloaded and installed all of the latest updates from Microsoft Update. Not really sure where else to look.