Hi,
Very interesting topic, here is my response, probably will maintain its zener voltage but the zener diode can be modeled as a voltage source in series with a resistor this is the differential resistance of the zener, this increases sharply when the zener current decreases below a critical value, this degrading the shunt stabilizer performance. For low power zeners i usually bias them with a minimum if 1mA in case of lowest input voltage and highest output current, a rule of thumb however states that the bias current should be 5-10% of max Iz, however this would give you 50% of the max dissipated power, if you bias with 10% of the max. dissipated power 2mA will be fine.
If you want the get into the details here's an interesting white paper: **broken link removed**
Summary: 130uA is to small, use 2mA.