Why did my RV rooftop a/c shut off when I unplugged the furnace?

Hello.
First, try to clean the board, perhaps humidity make shortcircuits betwen logic gates. Second check capacitor, if someone is inflated, replace it.

Please give make, model, year etc of RV that furnace is in. Thermostat on wall operates heat and cool?

remove filter etc. from ceiling assy, you'll see 4 bolts that you remove,(basically 4 corners of lower tray at ceiling) unplug wiring harness and connector, that goes to upper unit from lower, then lift upper unit up off roof. position upper unit to allow for removal of 14" gasket. Install new gasket, set upper unit back over hole align properly, and re-install 4 bolts. Snug evenly until gasket is approx. half thickness of original. Re-attach harness plug etc.

I'm not sure what the problem may be but you could try calling All Seasons RV Appliance Parts & Service. There number is 1-800-344-0673 they have helped me in the past. That and there tech calls are free so it wouldn't hurt to give them a call.

check thermostat wire and thermostat itself

Replace the thermostat it ain't no good no more

If this unit has a spark ignition you may just need to clean the flame sensor. It is a metal rod protruding in the path of the flame.

We hotwired the thermostat wires and the furnace started. That told us that the problem was with the thermostat. We took our remote control to another camper like ours and our remote worked their furnace. That told us that the problem was in the ceiling control for the furnace/ac. But the man who owned the other camper told us that he had a problem, too, and was told to unplug all the electric including the battery, wait 2 minutes, and hook up again. This might reprogram the circuitboard, and voila! It worked.

I had same problem. pressure regulator on furnace needed adjustment.