http://www.aximsite.com/boards/showthread.php?t=114593
It seems like if you have Pocket Outlook set to automatically check your mail, it'll try to do so even if the unit is "off."
Note also that "off" isn't really "off." If you just press the power button and the screen goes black, that's not really off. To make your axim actually turn off, you have a choice of removing the battery, or going to the 'power button' tab of Power Settings, selecting 'full power off,' then holding down the power button until the screen goes black.
EDIT: If you physically remove the battery overnight, and it loses a charge, then the battery itself is either worn out or defective, and you get to experience the unparallelled delight that is Dell Technical Support.