Thank you VERY much for the suggestions !

I did NOT restore anything. See below about hardware. Blech.
I attached two copies of dmesg output just after rebooting, a couple minutes apart. I don't have any clue about what's goiing on under the hood there. Or much else about linux, still.

>DSME handles the idle timer and I think there is a non-Nokia version you could try installing. Different
software might fix the problem.

I saw that people wanted to make one a couple years ago, but no results.

>MCE sits on top of DSME and Powerlaunch has a replacement for that, so try it too.

I installed Powelaunch but I couldn't find powerd, which I think is what you mean.

>Have you installed the community SSU and Diablo Turbo?
I already had the comm.ssu installed but I will try that again. I read the diablo turbo thread, well a bunch of it, and am not sure I understand how to install it, but will give it a try after the comm.ssu .

>If none of the replacement software works around the problem then you'll have to do what tgalati4

I'm not hopeful about that. I just remembered something else: before my reflash last night, I had Fanoush's initfs installed so I could boot from sd. But.... the time-out didn't seem to occur then.

That leads me to think it is some kind of software issue. Although, I guess if it is, say, a hardware clock issue, the software might only read it during normal operation and could be doing some kind of superfast timeout as a result.

Re:battery. I have had 0 battery problems thankfully so far. I guess it might be a litttle weaker but otherwise its fine. It does the same thing when plugged in. Would that be likely to make any difference? I guess the only way is to try it.
Again, much thanks.