It seems that the GE refridgerator really pulls the juice. Mine lasts less than a day on invertor as well. I plan to put new better wuality golf car batteries in as well.
Did you check the water regularly in the batteries?
I know it seems counter productive but... I keep cold packs in the freezer and put them in the fridge side when I want to stay on the invertor for a while and turn both thermostats to warmest setting to keep the fridge from cycling on so much.
Hope that helps.
Dave......
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2006 TourMaster T-36 / Good Sams / FMCA 380624
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