In a Voltage Regulator, what is it that decides the maximum resistance of the resistor and why?
If R is too large, there will not be enough current flowing through it to ensure that the zener diode is reverse biased with the correct voltage across it. 

The current through R divides into two components - Zener current Iz(nominal) and base current. Ideally base current can be neglected. And you will choose R such that the Zener gets a little more than the nominal current (10-20% more should be fine).

So R &lt; (vin - vz) / (Iznom * 1.10)