Just thought I'd update this. New battery fitted, 10 days on first charge, 11 on second, probably about 15-20 hours use each time - and that's a lot of page turns, I read fast. So it was the battery. That's OK then, I didn't get the life I should have from it, but a new battery is minor.
Now, does anyone know how to re-set the battery meter? It's going from 50% charge to "feed me" in one go. Not critical, but it's useful to know how much charge is left.