Thanks very much, NatCH, I tried your suggestion of plugging into it the wall, and almost right away the screen unfroze - after what seems like a hundred years, but maybe only 10 days or so.
So it seems that the freeze occurs when the battery gets too low.
I can confirm that the reset doesn't work when the screen is frozen. And another suggestion - connecting it to the computer - doesn't really help. (The connection isn't recognised.)