Hi David
answering questions in the forum is always a bit of a guessing game without much certainty, as one can't see the circuit at hand. In general the Arduino is extremely reliable, and what you are describing should not ever happen. Atmel would be out of business if their chips spontaneously reprogrammed themselves! While they do have a little stock-options problem at the moment, their chips are working fine!
I would poke around with your scope set to AC input, and see if there are excessive transients on the power supply lines. My guess is that the program is not "erasing" itself, but rather it isn't being allowed to start...
D