Sprint PPC6600 won't stay on when plugged into USB any more

[GnatGoSplat]

My Sprint PPC6600 (HTC Harrier) will no longer stay on when plugged into USB. It has the original PPC2003. I used to be able to use it as a nice desk clock using SPBTime and sitting it on its dock. It would always stay on, and has the checkbox checked to always stay on when plugged in. It has been fine for years. Now, it shuts completely off after awhile. If I turn it back on, it still turns itself off when left alone. The only way to fix this is a factory reset, which only works for about 2-days before it shuts itself off and will no longer stay on.

Any ideas what might cause this and how to fix it?

The battery holds a charge, so it doesn't seem like degraded battery life is causing it (I wouldn't think battery life is a factory when it's plugged in anyway).