Sounds like it's not a reboot, but that the Qtopia desktop is crashing and auto-restarting (from a terminal, try "killall qpe" for similar effect). Could be a misbehaving application or driver. Did you install anything "strange" to the Z?
Come to think of it, I now remember having a similar problem. I had installed a series of at-jobs to run every 15 minutes in the background to check my mail on the Z. Somehow my at jobs were causing the Qtopia desktop to crash intermittently. Unfortunately I can't remember the specifics now but maybe you can double-check your background processes.