Your A/C runs off 110V, not your inverter. It also has to have 12 V from your battery's, to run the thermostat, and that sounds like your problem, battery is low! Your inverter is probably not charging your battery's. Check the breakers on your inverter, to make sure they have not tripped, and check your battery/battery's state of charge. (SOC) Unplug from shore power, check your battery's SOC, then plug in and check them again, to see if they are getting a charge. Hope it is something simple like this! Rail!
__________________
Retired, and "Always on Holiday!"
1996 Monaco Windsor 38PB, "Mona" 275 HP., 8.3 Cummins, 3060 Allison 6 speed, 2001 PT Cruiser, "Bailey"