the ups isn't angry at you, some protection triggers or voltage loss detection circuit is not ok. if you're sure over-voltage/current protections are ok without identify them and put the scope or the meter at work, then go with voltage detection branch and test that
the ups logic may be different when you power without mains present (doing validation checks and starting the inverter) and when it has mains but it looses it, those checks may be done differently by the ups firmware. why? because starting inverter from batt is different from switching from mains input to starting-up inverter, put yourself in designer's head
in your place, i won't eliminate without putting the meter at work...
i don't know your ups, a relay with contact problems also can give symptoms like this (dunno if they commute with mechanical relay or triacs or what-else different)