Why would unplugging an A/C unit restore power to a circuit?
I believe what Kris is saying is perhaps you should look at the back of the AC receptacle. Are the wires going to the plug all on the plug? If there are more than two blacks in a box we usually marrett them together with a pig tail that goes to you receptacle screws. Some people go the lazy route and poke each wire into the back of the plug, instead of making a pig tail. Over time things can become loose. I don't know how the brownout could contribute to this but electricity can be finicky in ways!