I'm happy to report that I think I finally found the culprit that was making the Device Manager refresh. The Crashplan backup service! Every time it scanned for things to back up it did a scan for new devices attached, disconnecting the gamepad in the process. I have set it to only back up from 6 AM to 12 PM, and tonight I was able to play without any gamepad disconnections for the first time in weeks. If you run Crashplan or something similar, try adjusting your settings to see if this problem goes away. I know it might be different for others, but if this does turn out to be the solution to my particular problem, I will be very happy indeed.