RV Furnace Intermittently Works

If your furnace is the original to Motorhome and has not been changed or replaced, then it is around 24 years old. The likely suspect for the rudimentary description you gave of the symptoms gets my suspicion that the "time delay relay" is wearing out. One symptom is longer and longer periods from cold start, that is, not having run for awile. You turn the furnace on, later the blower comes on for a period, then the igniter fires up to lite the propane for furnace operation. The delay should not be a long one as it is to assure that all and any residual gas fumes are purged from the area of furnace before ignition. So long as the blower is fully operational as opposed to slow speed for lack of sufficient power, or that it cannot get up to speed and the sail switch cannot fully function. But that is a different issue from yours. This delay is all part of the operation of furnace whether cold startup or ongoing cycles. Your retriggering the thermostat is triggering the relay and shocking it to resone correctly. Eventually even that will not work. Time delay switch replacement is a simple one for installation and is not a very expensive part. Please let us know when you track down the culprit.