IMHO it's not ideal to have the inverter restart or even shut down.
More expensive inverters (and not by a country mile), will allow for grid pass thru of up to 56A in some cases, meaning that you will never be "disconnected" if the demand increases beyond the inverter's output.
One never knows what unexpected load condition may occur.
The Axpert can tolerate 8kVA. There is an option about strictness on bypass mode.
But honestly, if you are overloading you are doing it wrong.