Sowers: gave it a try, the first time it seemed to wake up, but then it continued with its bad behavior. There's a window where if I wake it up shortly after it goes to sleep, it will come back. But if it goes longer, it won't come back unless I remove the battery for an extended period of time.
Jim: Yes, that's the conclusion I'm coming to.
Thanks for everyone's input. Time to get a working one.