I've had an Arduino-based ATmega168 running an RFID garage door entry system for over a year now. It's been rock-solid even when the outside temperature was -10F.
One of the key things to remember is that a programmed chip starts running its program on power-up (after a short bootloader delay). So even if you have a power outage or some other kind of "reset", your device should automatically return to a functional state. The only exception to this would be time-critical or real-time types of needs. In this case your biggest concern is power stability, not the ATmega168.