This issue is caused by installing one of the following updates that have been pushed out by Microsoft on 11/12/13: KB2837618 or KB2837643 If you have not already done so, please avoid this update for a bit until Microsoft corrects the issue.
If you cannot avoid the update, we will provide you with further steps regarding a temporary fix for the issue.
This would allow them to review the email logs for errors/problems.
I also found a similar question in the Official Outlook forums, where they are discussing this issue.
This issue with Microsoft Outlook 2013 and Office 365 will cause IMAP folders to not successfully synchronize, therefore inhibit your ability to receive new mail to your inbox.
There are a few ways to resolve the issue: One option is to remove the recent update that has been pushed out by Microsoft to Outlook 2013 and Office 365 users.
Changing it back to the original setting, should allow them to see the original folders again.
Here is a link to the official Microsoft guide on how to Choose which IMAP account folders appear in Outlook.
Thank you, John-Pauljeff, after a week including Microsoft paid for support, you struck it with the second option of disabling the subscribed folders.
i don't know how these solutions are found sometimes, but you should take great pride in this solution.
Visit your Account Settings, then Advanced for the mail account that you are having trouble with.