I figured out that it was my Titanium Backup program that was doing a force kill on the program so it could back it up. So if you have the same issue with BeyondPod feed update getting disabled all of the time, just go into your titanium backup program and either create a filter so it doesn't backup BeyondPod, or change the settings on Titanium Backup so it does not force kill applications. I would suggest creating a filter because if Titainium Backup doesn't force kill the application it won't be able to back up many programs properly.
Later,
-Spader