This circuit won't really prevent draining the batteries. I suggest a solution involves 1 power PMOS, one NPN BJT, one Zener and a few resistors. Make the BJT conduct and pull the gate of the MOSFET low only when Vbatt >= Vz+Vbe.
simulate this circuit – Schematic created using CircuitLab
The Vz of TL431
can be tweaked using a pot.