12.8 volts is a fully-charged battery at rest - an inverter shouldn’t shut down unless it goes below 11 volts or so. Are you sure the voltage isn’t dropping below 11 volts or so when you put a big load on it (measured at the inverter, not the battery)? It will drop quite low if the wires leading to the inverter are too small. Also, is your battery bank capable of delivering 200 amps? Check the battery specs. Below is a wire gauge chart. 200 amps requires some very thick wire, and short runs of wire.
