how voltage references work - LM336
In normal operation, you would be feeding reverse current through the device, so the Absolute Maximum Rating would be 15mA; the line on the reverse-voltage graph stops at 10mA, but it probably extends pretty straight up to 15mA.  Not that one should operate the part there, but one probably shouldn't worry if current gets up to 11mA.

On the other hand, in most cases there's probably not much point in driving the thing with more than 1mA.  The graph suggests that the voltage drop will be pretty constant provided there's at least ~0.4mA flowing through it, but the voltage drop falls off very rapidly below that threshold, so one needs to ensure one is operating safely above it.  To allow for part variations, 1mA seems like a good safe operating level.  The only time I can see usefulness to going above that would be if one has a load whose demand might vary e.g. from 0-8mA.  In that case, one might drive (part plus load) with 10mA and figure that the device would have 2-10mA passing through it.  Voltage should remain constant provided the load current stays below about 9.5mA.