First of all I suspected the hysteresis width to be small of only 0.1V and tried increasing the width in search of better performance. I tried setting the upper and lower threshold voltages to 3.6 and 3.45 Volts respectively which is equivalent to battery being fully charged at 14.4 Volts and discharged at 13.8 Volts. But the problems still persisted. If the voltage is rising from 3.45 Volts, the op-amp's output changed before the voltage reached 3.6 Volts at around 3.55 volts. And while the voltage was decreasing from 3.55 volts, the op-amp's output changed before the voltage reached 3.45 volts at around 3.5 volts. The same problem persisted with the upper and the lower thresholds at 2.4 and 2.3 volts respectively.
Really stuck on this one!