[Arkware]

Question: Does the inverter shut down OR does the gfi trip? The inverter should tell you...
If the battery voltage is low or dips, ( 12.0 volts is low) the inverter will shut down.

You may have weak batteries.
In my case, the dealer supplied Marine/RV batteries just didn't hold up.
Need batteries rated in Amp/Hours not Cranking amps, and several of those.

Is the Ice Maker turned OFF while running on batteries?
It uses a bunch of power and will greatly shorten battery run time.

I don't have any solar panels... but my research says that one panel is not enough to run the fridge.

I hope this helps,