Help - Battery discharge protection circuit
BeB00 is right, your schematic will not work as it is simply keeping the transistor turned on, and the zener is not even doing anything there - it would be the same if you removed it, no change in circuit behavior.
 Here is what BeB00 has suggested to you (plus my own suggestions):


The way it works is that the battery voltage has to be above the base-emitter voltage of around 0.6V PLUS the zener voltage of around 2.7V in order for the base current to flow through R1, the zener diode and the base of the transistor, which in turn makes the current flow through the LED1, R2 and the collector to the emitter (ground or negative side of the battery).
 The second LED (LED2) is an option if you can't find or get a 2.7V zener diode, and it has be a blue or white LED which has around 2.7V voltage drop in this circuit (you would have to measure it once you place it in this circuit).
 You could also use 5 standard diodes (like 1N4148, 1N4001, or any rectifier or signal diodes) instead of the zener or LED2, and you would have to connect all of them in series and in forward direction like the LED2.