Chronic problem with Atwood water heater

Is your TT parked in a spot where there is high humidity? It may be that the mechanism of the thermostat is oxidizing and then becomes stuck. If it was my problem, I'd replace with a new thermostat, forcing some anti-oxidant into the thermostat. One of the best anti-oxidants for this purpose is Caig Deoxit Gold. It cleans up any oxidation and provides a barrier to future oxidation. Available at Radio Shack in a spray can. It works wonders for truck/trailer umbilical, too!