If everything else is good and the consensus is the t-stat, I'll throw this into the mix:
Could it be that the make and model of the t-stat you are using does not perform well in an RV environment?
Why do I ask that? I owned a S&B house in NH with FHA heat. Without a humidifier on the furnace, static electricity was a problem throughout the house in the winter. When I went to replace the old round dial t-stat with a setback t-stat I bought a Hunter (brand) t-stat for something like $39. I don't recall the model #. The tiniest static discharge from a finger touching its control surface would erase all of the programming that I did. I returned it and bought a
Honeywell CT3400 setback t-stat for $99. At the time I thought $100 was too much for a t-stat. IIRC, it was advertised as resistent to static electricity. It is. I would drag my feet on the carpet, touch it, and generate huge - mildly painful - shocks and nothing hapened to the t-stat.
Where am I going with this? If you replace it with an 'old fashioned' t-stat, similar to one of these, and the furnance works fine - then research the available t-stats. Test 2 or 3 of them. Look for a ruggedized unit designed for hostile environments. It just may be that the one you bought sucks, or is not well suited for the application that you are using it for.
