I also ran my propane fridge in my small travel trailer under way going to hunting sites, etc. without issue, but was careful to turn the flame off when using a fuel island getting gas for the truck. Never had any problems with it staying lit either, but did keep the burner clean and free from debris -- and I will say that towing the little trailer on the forestry rock roads did shake out plenty of scale from time to time.
My Tour Master coach had a residential refrigerator, so no open flames while traveling with that...
2007 Tour Master T40C
Acura MDX toad
"It takes a great deal of time to recover from any improvement..."