ac and fridge need 12 volt to run thermostat. ac will come on but when it reaches the set temp and shuts off it can not turn back on again if there is low 12v going to it. The voltage only needs to be off just a little for the thermostat not to work correctly.
You might have a low voltage problem. Check that your converter is charging your battery and/or check that your coach battery is not shot.
Also don't flip the temp up and down or flip the on switch on and off. The ac has a delay. You are screwing that all up by flipping it on and off and temp up and down. Mine has such a long delay before it comes on that to this day I still have heart checks that it's broke. Only to have it come in a few minutes.