I'm testing out an inverter series that has on board 120 vac chargers on them. I noticed if I run my inverters to the point where my batteries ( lithium iron phosphate, 12v ) empty out below 12 volts, it will shut down the inverter. Which that I am okay with. But the problem is, if I plug my inverter and attempt to charge it using shore power, the inverter will not charge the battery at all. It needs the 12 volt to be working, so it can switch to 120vac charging. Needless to say, if I parallel another fully charged battery to the array, the 120vac switch will flick on, and the battery will start charging. Then the charging will continue regardless if I take away the extra battery or not.

Is this a regular occurrence for inverter/chargers? Seems like an awful flaw on the manufacturing side of things...