The App Nap feature included with Mavericks and Yosemite appears to be buggy with some Outlook 2011 setups. It has been reported to cause Outlook to frequently forget account passwords, repeatedly lose connections to Exchange servers, and massive email duplication.

The confirmed fix for this is to disable App Nap. To do this, navigate to the Outlook 2011 app (/Applications/Microsoft Office 2011/Microsoft Outlook), do a File->Get Info on the app, and check the “Prevent App Nap” checkbox.