First thing, you have to understand that the
battery meter that is reporting the state of charge (SOC) doesn't really know that number. All it does is measure what goes in and subtracts what goes out. If the batteries are not of the same capacity as the meter was told (i.e., they are old and failing) the actual SOC will have very little to do with the reported value.
Now... what cuts off the
inverter making AC current is low
battery voltage. Do you know what the voltage is when the AC is shut off?
It is POSSIBLE that value is adjusted too high in the inverter settings, but it is far more likely that your batteries are actually nearly dead. What the meter thinks is 90% full is actually much, much, much lower.