First I would try replacing the battery... a weak battery could cause this issue. Of course, it's a built in battery, so that may not be easily done unless you have another zire 72 around.
If the battery meter on the palm says that it has a good charge after you charge it, and everything else works fine, it's probably not the battery.
If that doesn't work, try a soft and hard reset to see if this fixes your problem. (Information about these can be found in your user manual). Be sure to back up your palm before doing this as you may lose your data. (You WILL lose your data doing a hard reset).
If neither of these works, my guess would be that you have a defective clock chip in the palm that doesn't keep time accurately. I would call PalmOne about this and see what they say, AFTER doing the resets that I suggested.
I've never called PalmOne, but I hear they sometimes have long hold times (1-2 hours)... so bring a book 
