Can fridge run on propane while you are towing 1500 miles?

I kept mine on during our entire trip from Jersey to Florida, stayed 11 days and then on the way back and aside from the freezer getting over frozen because we had the temp setting to high for max cold it kept everything ice cold. We did have to keep the fridge off and open for a few hours to thaw it out and clean it ALL out before storing it away and then of course wouldn't you know it I went back the other day and found the battery dead as dead battery can be.