I'd been doing some mods in our 21NE and wanted to be comfortable in the heat of the day. Over 3 days I had the A/C running, originally with a 14/2 extension cord that I had in the garage, and noted the A/C was not running smoothly, with the compressor kicking on and off sporadically.
I hoped it wasn't a failure developing with the unit, since it was barely a year old with maybe 3-4 hours of usage over that time. I wondered if the length of power cord and the gauge were causing this issue. I felt the cord and plug and found it quite warm. It wasn't handling the demand load of the compressor as it kicked on and off. Not enough to kick the breaker...certainly enough to disrupt the units operation (and potentially causing damage) but certainly a potential fire risk.
I had a 12/2 cord purchased specifically for use with our Honda 2200 generator and switched over to the heavier cord. No problems after that, no heated up cord, no A/C acting funny and nice cold air being generated safely.
If you are using a heavier cord (i.e.: 12/2) and 50ft or less, you shouldn't have any issue operating your A/C unless there's other heavy loads on the same circuit. And before you ask, the trailers 30amp cord won't reach the 15amp plug...thus the extension required.