I had the same problem with a cheap MSW inverter I initially purchased when first setting up my off-grid sytems, it was dragging huge amounts of power even when off and it was harming my batteries. I replaced it with a (much more expensive) better brand TSW inverter/charger and my problem was solved.
I also modified the connections between my batteries so that the power draw was evenly spread.
I also modified the connections between my batteries so that the power draw was evenly spread.
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