Okay, here's what I've gathered:
1. I assumed the same thing, so I ordered a new encoder battery. The robot loses its 4th axis calibration only after being turned off for a long time - two days or more. The battery hasn't been replaced in at least three years, so this may be the cause of the problem (although it's strange that it only affects one axis).
2. I'm zeroing the robot based on its markings at the end of each axis. I can't remember exactly which function did the zeroing (I think it was 45, but I'm not completely sure).
Also, how can I download the backup? Until now, I have only been working with newer controlers from Kawasaki that have a new TP and menu (E series). I hope I don't need an RS-232 interface on my laptop to download a backup, as I don't have one.