RE: lipo charging problem
Yes, but that is under a load. The voltage sags under load and depends on current, connectors,leads,load, ect.
Try a resting voltage check after it hits the cut-off and then after it is charged.
It may very well be hitting the cut-off yet the battery is still more than half charged. In fact it is probably over 80% still charged. The two voltage checks will tell the charge level very closely.