I doubt there is a cut off on the HV battery regarding SOC% more likely voltage sensing.
Lead acid batteries are very slow charging, especially the last 30%, the last 10% can take up to 24 hrs to charge to 100%. Because the genuine 100% isn't reached regularly, the plates begin to sulphate and the actual available capacity drops ......
Think of it as a water tank slowly filling with sand, the water runs out the top and you think it's holding the full capacity, but the tank could be 80% full of sand .... the water will still run out the overflow, but there isn't the full tank capacity of water available, only 20% .... and you suddenly run out of water unexpectantly .....
Putting a reconditioning charger on the 12v battery will flush out the sulphur from the active lead plates and return the capacity ..... as long as the battery isn't left too long or ever reached the point of being so sulphated there was not enough capacity to power up the system .......
Lead acid batteries are cheap, but definitely not suitable for electric vehicle aux batteries, sodium ion would be the ultimate option, they can handle being deeply discharged without damage and recharge fast, the 14.3v +/- even 0.5v would still be within the upper safe range for a sodium ion 4 cell battery ........
Maybe I should design a replacement battery for EV's and hybrids like the Prius, they have a very expensive battery that simply doesn't last ......
T1 Terry