Low SOC in the battery.
Battery current discharge limit exceeded.
Volt drops in connections, cable, breaker, fuses between battery and Inverter.
Inverter settings , if available, for low volts disconnect set too high.
Faulty microwave.
Faulty Inverter.
Assuming everything worked with the old setup then it's down to the changes made to the system.
Investigation with a multimeter and DC clamp meter should identify the cause.