What brand and model of device? There's a big difference between a surge suppressor and a power management system. With a power management system, there is usually a startup delay and it will cut the power for over or under voltage. If you don't have the problem with the unit out of the circuit then it is defective.
The reason your A/C is cutting out is because the compressor motor is drawing too much current to try to compensate for the undervoltage. This causes the motor to overheat and possibly go into thermal protection (if the overcurrent doesn't trip a breaker first). Assuming the fridge is a domestic (i.e. home-style, AC-only) its motor is likely overheating for the same reason except that the fridge motor is usually a much smaller fraction of the circuit capacity so its unlikely to trip a breaker.
You need to fix the undervoltage problem (stop using the device if that solves the problem) or you're going to let the magic smoke out of some of your appliances.
2015 Rockwood Signature UltraLite 8282WS Platinum, GY Marathon LRD, TST 507RV TPMS
2005 GMC 2500HD CCSB D/A, Curt E16, Prodigy P2, Garmin RV760LMT w/BC-20 b/u cam