All shared mailboxes attached to a users' Office 365 Exchange account suddenly stopped updating in Outlook. The user can still send emails via shared mailboxes, but can't see the email they just sent in the in sent items folder. Also, no new emails show up in Inbox. The user's own mailbox is working fine.
The issue was resolved by unchecking "Download shared folders" option in Advanced Exchange Account Settings
This basically disables cached mode for Shared Mailboxes. The main user's account still can work in the Cached Mode (if you leave "Use Cached Exchange Mode" option enabled). If you have to have Cached Mode for shared folders, re-creating an Outlook profile would probably fix the issue as well (although I haven't tried this).
MS Office 365
MS Outlook 365