The voltage level of batteries slowly decreases as you use up their power. Below a certain voltage your memory chips will lose all their information. The Palm machines minimise battery use by going into sleep mode as much as possible - even when the screen is on the CPU may be asleep.
Playing games that perform lots of computation and have high screen refresh rates (eg. Reptoids) is the fastest way to use power. Use of the backlight only doubles power use for a light load program.
Even when your machine is not in use there is a small power drain, needed to keep the memory alive and to respond to buttons being pressed to wake the processor up. In addition there is power loss due to natural self discharge of batteries - this occurs even when they are in their packaging.
Don't leave your PalmPilot in a drawer or cupboard - use it regularly, then you can act on the low battery warnings: insert new batteries when warned. If you leave it at home when you go on holiday make sure that there is enough power in the batteries before you go - fit a new set if necessary.
Run The Memory Too Full
Many applications need extra working memory to run in. If you run at too much above 90% full you can end up crashing.
Use Rechargeable batteries
They can save you lots of money (I use them) BUT they lose power very quickly at the end of their life. Download and use a utility to change the automatic warning and shut off voltage levels to higher values than the default settings. The default levels are for alkalines and are not appropriate for rechargeables. (I set mine to Warning at 2.2V, Critical at 1.98V). Carry a spare set of batteries with you at all times if you use rechargeables. If you don't do this you run the risk of an alarm causing such a rapid drain of power that the batteries dip below the Voltage required to maintain the memory.
Trial Lots Of Applications
Eventually you will load one which crashes on you, or which corrupts memory and causes a standard application to crash. Some applications are badly written, I have had my address book crash every time I opened it, I cannot believe that this was a 3Com fault.
Take Out The Memory Board
Taking the memory board out disconnects it from the batteries and back up capacitor. No power wipes out all the contents of your memory.
This is the quickest way to wipe your memory clean - intentionally or not.