If you were on shore power (at home say) the battery disconnect should already have been at "connected" and the inverter/charger "on" with charger "enabled" so the batteries would stay charged up at home, being "maintained" by the charger.
When you are on the road with just the 7-pin charging the batteries, that is at trickle amps, so the batteries won't get much support for running the fridge etc. The batteries would have to be charged up already for that.
? Perhaps ? Your batteries were low from not having being on the charger when at home, and the inverter could not get enough DC to run the fridge with just the 7-pin helping. The inverter will have a low DC input voltage cut off.
If so, your batteries are in trouble, and need a good recharging "recovery" session (same as equalizing procedure) to get them back in shape.