After charging you should let the batterie sit for an hour or two and then check the voltage. If it´s too low the battery is past it´s prime. It is important to let battery warm up before charging. Otherwise the battery may not be charged to the full capacity. The car battery may need a night in a room with a temperature above freezing before it is warm.
Sometimes the contact where the ground strap of the battery is attached to the car´s body is loose or corroded. That may also cause the problems you described.