Doesnt look like it has a battery for the clock, but it makes sense when you run out of battery and your Z boots up it asks you to check the time. You can test that by clicking reboot and when the screen turn black remove the battery, wait 5-10 min then start the Z the time wont be right and you'll get a: ADJUST CLOCK warning on the time app.
I remember my Palms always came up with the time settings app after a softreset, not when on/off (suspend), could have changed never had a PalmOS5 Handheld