I don't think it is the inverter, I have not measured it yet but I believe there is at least 6' -8' of wiring between the batteries and the inverter and maybe, just maybe the voltage loss is to high for the inverter to be able to produce 110Volt ac when the fridge compressor starts up. Our trailer came with 1 battery from the factory then the dealer installed two 6 Volt AGM's and a local battery/solar shop installed 4 more and our solar setup. So, maybe someone replaced the wiring to inverter but I won't be able to figure that out before tomorrow night.
I have 12.8V - 13.0V across the battery bank but only 12.2V - 12.3V entering the inverter, the shutdown happens at 11.8V at the inverter. I don't think it is a battery or inverter issue it is probably wiring related.
Edit: The res. fridge is a lot more reliable than the Norcold, use the money you safe on the fridge and install solar panels and upgrade the batteries. With our setup we do not need shore power or generator unless we want to use the oven or AC.
2013 RAM 3500 Dually Longhorn
2014 Trilogy 3650RL, W/D, Onan 5500, 8000# Axles, IS, 960 Watt Solar, 6x6 Volt Battery Bank, Freedom SW 3012 Inv/Charger