Could be low voltage, it has to be tested under conditions that represent the problem load.
I plug an AC voltmeter into one of my interior outlets, monitor readings under various loads. While it is not the same circuit as the air conditioner, it provides a good clue as to what is going on between the breaker box and the power source (measuring at the source usually just tells me no-load voltage).
I want to see at least 108 V inside when running the high loads (nominal is 120 V), no more than 132 V with no load. I also want to see only a small drop from post to inside under load, as large voltage drop suggests a high-resistance connection somewhere: socket or plug, cord connections at junction box, connections inside breaker box, too much cord too small. Problem connection can be either live or neutral. High resistance connections often don't show up with no-load voltage readings, or even light loads.
