We have one user in the company that has 2 mac computers, an iMac, and a macbook air. Both are running 10.9, Outlook 2011 (current update), and are not receiving any new email in their inbox on the computers, but is receiving new emails on his iPhone and iPad. His mailbox database size on exchange has not been reached either. His Outlook 2011 account has been rebuilt, deleted, and recreated, but the issue continues.
If he clears/empties the cache in Outlook 2011 this works for a little while, but the email stops coming in. His inbox is around 16Gb, if that helps anyone.