This is my problem also, using Outlook for Mac in Office 365 configured to IMAP. I contacted my mail server who researched the issue and gave me the following reply:
"Thank you for your reply, the folder itself, but that is more of the solution for a windows system. We are usually not required to help with third-party issues but after researching a bit I think I found similar issues and possible fixes, the first should be:
1) Tools > Run Schedule > Edit Schedules
2) Assuming you already have a scheduled "Send/Receive All" occurring every few minutes - double-click the appropriate Schedule item.
3) In the Edit Schedule window, in the Action area to the right of the Receive Mail action, click the Account Options button.
4) Put a check next to every folder and in the Synchronization Setting column make sure it is set to New Messages. If you choose Headers Only, the folders will not auto-sync.
If the Account Options button is greyed out, then you have updated past the need to have a schedule run and can simply press Control-Click>Synchronize Now. Also you will have troubles with any folder that is over 2gb in size and you may need to start removing or archiving emails.
Your webmail should load and work fine though."
I got as far as step 3 and did not find an "Account Options button" but the "enable" button for "Send and Receive All" on the "edit schedules" menu was unchecked, so I checked it and I'll report the results. I usually get several of these messages a day so if there are no further messages over the next couple of days this will probably have solved my problem.
