I don't think you lost water pressure, as it's usually a closed loop, but rather water flow.

You said your A/C isn't on a battery or generator, so it should have been off while the water wasn't flowing. Perhaps your A/C restarted as soon as the power came back on, the water didn't start flowing right away, and your compressor kicked out. How the water starts flowing would be a question for your building people. A baseball bat might help you get info from them; I find it's like pulling teeth. It takes less than 3 minutes without water flow for our unit to go into overload protection, so we have a few minute delay on our A/C startup to give the water a chance to get moving.

-jk