check Options \ Auto On/Off
If it's not that and you replaced both the battery AND the device, then it is a setting somewhere or perhaps a 3rd party app you have installed
does it happen daily at a set time that you can watch for it to happen again? Did you use a restore file from previous BB? I would guess that the "setting" we are hunting for was saved in that and carried over across all your replacements. If you can, I would wipe the device and not reload the restore file, then watch for it to still happen. If it does not happen you can slowly restore parts of the restore file under Advanced in DM until you determine which database is causing the problem