Power outages do not damage an appliance. Newer refrigeration should have a delay circuit so that frequent and repeated power cycling does not damage its compressor. Power outages and surges are two completely different and separate issues.

Adjacent protectors do not claim to protect from typically destructive surges. It can even give a surge even more destructive paths into any nearby or attached appliance. Effective protectors also never fail on a surge. Only near zero (undersized) protectors fail.

Protection must be at the service entrance with an always required low impedance (ie less than 10 foot) connection to single point earth ground. (That is not receptacle safety ground.) Only effective protectors have that dedicated wire for a low impedance (ie hardwire has no sharp bends) connection to earth.

Surges must be earthed BEFORE entering. Otherwise a destructive surge is hunting for earth destructively via all household appliances. And finds a destructive path via only one or some appliances. Protection for any appliance mean all (ie dishwasher, LED and CFL bulbs, recharging electronics, bathroom and kitchen GFCI, furnace, TVs, washing machine, smoke detectors) need that protection.

Appliance protection has always been about that destructive current not anywhere inside. Nothing on an appliance power cord even claims to protect from that transient.

Previously, a destructive current was via a relay. That is unusual. Damage is more often on electronics that drive a relay. But if damage exists, then that part was in a path from AC mains to earth ground (maybe via pipe that connects to an ice maker or via contact with an electrically conductive floor such as concrete or linoleum). Anything that can might make a connection to earth is on a 'suspect' list.

A mechanical part that must have hysterisis is a thermostat. These are generally sealed units. However examination may find a screw that can adjust that hysteresis. It should close when temperature rises. Then not open until temperature drops significantly. Your thermostat may have very little hysteresis. Therefore a thermostat will open after slight temperature decrease.

Unplug it and leave it to warm inside for at least 10 or more degrees. Then plug it back in. If it runs for a long period, then hysteresis for that thermostat is a prime suspect.