A scope with infinite persistence and qualified triggers can help capture
random events. I would use level triggering on processor power, say
start with .5 V out of spec low, to see if you get any triggers. Then do the
same for .5V out of spec high. Do the tests letting scope run for an hour or more.
Are you confident you have proper power supply sequencing, no pin on
processor presented with a V outside its supply rails ? That can trigger latchup
which clears when power is removed and or supply bond wire internal to package
fuses open.
Regards, Dana.