Damaged glass shield of diode
Even with a photo (hint) it would be difficult to say. 

If it was removed from circuit you could hook it up to a bench power supply and figure out it's reverse breakdown voltage. Since the device is weak I wouldn't attempt to remove it unless the whole circuit had ceased operation and an attempt at repair is required.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Test circuit.

Test the Zener with your multimeter diode test circuit. You should get 0.7 to 1 V in the forward direction and open circuit in reverse. If that's good then ..

Hook up the suspect zener as shown. You'll have to guess what voltage to test with. 12 V would be a good starting point. The voltage on the multimeter should be the reverse breakdown voltage. If you read the same voltage at both ends of the resistor then the Zener hasn't conducted yet so you'll have to raise the voltage.