hey
Atmel has an application note here about corrupted flash memory. It is for the C51 series of microcontrollers, but it seems to say the same thing the EEPROM corruption support doc posted above says: brown-out detection.
D
PS if you want 24-7-365 reliability, you might consider designing an industrial-style Arduino, with optically isolated inputs and outputs, and a guaranteed fast rise-time power supply. There might even be a market in selling it 
If rise-time is indeed the issue, what about using 4700Uf of supply capacitors ( or even a 1Farad?) and then using a long rise-time R/C combination on the reset pin.