If you had the fridge set to auto, then it should have switched to run off propane. Running on shore power, the fridge 120vac heater will pull around 4 amps. As noted above, 12vdc battery power is needed by the fridge to run the fridge electronics. If you only have a single battery, you can't expect much run time without the converter charging the battery. If your battery/s are near 4 years old or have been discharged below 50% at times, then they may well be on their last legs.
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2012 F350 6.7 L dually, 2013 3800RE with 6 pt leveling, Sumitomo 17.5" load range h tires, Samsung 18 cu ft residential fridge, 8k Morryde I.S. with disc brakes. Full timing since 2012.
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