JIC it helps anyone else out there. For no apparent reason, Outlook 2010 started taking hours to download emails that usually came down in minutes. And when I say hours, I mean 3-5 hours! The app would remain responsive for the most part, but would consume 100% of a CPU/core. It would download a number of messages and then just pause for 45 minutes or more.
Turns out that the problem was my configured %TEMP% directory was filled up with almost 65,000(!) entries. An automatic update of my Antivirus software failed, and started looping retry attempts. This filled up the temp directory with little 1KB files until it crashed. It also filled up my event log.
Seems that Outlook gets really cranky when it has trouble with its temp directory.
So if you suddenly start having strange issues like this with Outlook, make sure your temp directory is not too full.