I again learned what I did last year when my laptop kept spontaneously shutting off. To really exercise and teach the battery what its capacity is, you need to drain it completely, until it goes into sleep mode, then charge it. Maybe even do it twice. Resetting the power controller (the hold the power button without the battery in thing) was not the solution.
Sure enough, it seems to do the trick. I haven't had any random shutdowns since. That's good news, because as I've mentioned before, I want get a full three years out of this thing. It remains as my favorite comprooder ever. Until I get the next one, next year. :)