Some chargers and inverter/chargers have a problem 'reawakening' a low voltage cutout tripped BMS. The BMS blocks any further discharge but turns on a path for reverse current charging.
There is typically a diode and a power resistor to limit the initial charging current which is a safety requirement for an over discharged lithium battery. Once all the cells gets above about 3v the BMS bi-directional switch reengages resetting the BMS.
Because of the initial high path resistance, due to diode and power resistor, the voltage as it appears to the charger rises quickly faking out the charger to believing the battery is defective. If charger just drops back to float voltage the battery will charge and eventual reset the BMS cutout. Some chargers are 'smart' and detect an abnormally fast voltage rise as a bad battery and just terminates charging.
An inverter/charger that actually has a Lithium Ion battery setting option may truncate charging when battery voltage seen by charger hits the maximum charge voltage, again termination charge current before battery has gotten enough charge to reset BMS. The inverter/charger may recycle a new charging cycle and eventually the battery will reset BMS.
Some inverters just sit in idle mode when battery voltage lost and/or reapplied, waiting for user to manually tell it what to do. Actually I prefer this as it forces you to determine the cause of what should be classified as an abnormality.
There are a few inverter/chargers that will totally shut down if battery voltage lost so no charging and you are really F'd if you have this situation.
If you find yourself in this situation a CV/CC limited power supply will get the BB battery to charge and re-engage BMS.
This is why you should carefully set inverter low voltage shutdown so it trips before battery BMS. Having too much battery cable resistance makes this very difficult when heavy inverter loading causes voltage drop at inverter input terminals.