terryking228:
Quick possibility is add large external capacitor on the 5V from the adapter. Say 4700uf at 10V or more...
I was thinking something along the same lines. Or a recharging internal battery with enough charge to keep it going until the electricity is stable once again, so that watchdog can reset it. Or have some sort of hardware monitoring for voltage, and have it send a reset signal to the reset pin of the arduino when the voltage stops fluctuating.