Outlook 2011 has problems with OS X 10.9 and POP email accounts. Many people have reported frequently getting the error “Connection to the server failed or was dropped” or “Inactivity timeout”, and often times messages will keep downloading over and over again causing duplicates.
The confirmed workaround for this issue is to disable App Nap. To do this, do a File->Get Info on the Outlook 2011 app, then check the option for “Prevent App Nap”.
This behavior seems to be limited to POP accounts. IMAP and Exchange account are not effected.