I've seen a couple of other threads but they didn't seem to quite describe my situation.
My wife has an '02 Camry. The battery is less than a year old and tests fine. I also installed new terminals and cables when we did the battery as the originals were tired.
For the past two days, the car won't start in the morning. No lights, no clicking. It's as though the battery was totally dead. So she comes inside to tell me, and the alarm will suddenly start going off. Switch it off, and the car starts right up. Clock and radio are both reset, indicating the battery was somehow disconnected.
The mechanic on the way to work couldn't find anything wrong with it.
Repeat that performance today, although it took considerably longer for the alarm to start.
One interesting aside. I was able to wake up, get dressed, open the hood, and touch the battery before it came back today. I was testing the cables to see of they were loose, and I swear it shocked me.

I've been messing with my old Alfa Romeo long enough to realize when it might be a grounding issue. Where's the main grounding strap in this car? Or maybe a separate engine ground wire?

 

It sounds like you are honing in on the problem being a ground. The ground strap from the battery shouldn't typically travel too far, usually just to the chassis. Which cable were you touching that caused the shock? It is weird that it shocked you as you should be able to touch the terminals all day as long as you are not connecting the two. I'm sure you know that though due to tinkering with the Alphas. Just be glad that none of the Alphas have Lucas parts in them! And be glad Camry's don't either or we'd be totally screwed!