I'm not familiar with the Power hub, but looking at the manual, I found this:

As long as the battery voltage is between 11.0 Vdc to 15.0 Vdc, the inverter will continue to deliver AC power to the loads connected to it. When the battery voltage falls below 11.0 Vdc or rises above 15.0 Vdc, the PowerHub 1800 High or Low Battery Protection will engage and shut the inverter off, stopping all output voltage to the loads.