I'm experiencing the same symptoms. Not sure what year and model your RV is, but take a look at this thread:
https://www.irv2.com/forums/f54/dome...es-612590.html
As you will see, I've pulled and bench tested the furnace outside the trailer, replaced the sail switch, and tried a new thermostat.
It would appear that the control module in the AC may be bad.
If you have a newer RV and are running the Atwood/Dometic furnace and AC it may be the control module.
Climb up on the roof and pull the cover off the AC and ensure that no "critters" have chewed through any wires also.