Hi Dale, What ignition system are you using?
If Zener diode goes short circuit, it will blow fuse or melt wire harness if too large of fuse is installed. It Diode goes open circuit, the battery
can overcharge. However if you ride with headlamp on all the time & have incandescent normal BPF bulb, the lighting system draw is such it pretty much uses up the current such Zener is not turned on or barely turned on. Unlikely Zener is cause of dying.
As suggested your volt meter or even a cheap test light is needed to see where the fault is. Sometimes with only a whisker of wire, volt meter will show ok, but test light will be dim indicating a poor circuit.
Whatever you do, don't buy anything as a guess. You want to find the real root problem(s) & correct them. That leads to a real repair that will leave you with very reliable machine. Also is by far the most cost effective way to repair.
Just because the fuse looks good visually doesn't mean it is. They can fracture under the end caps, plus fuse holder can be faulty. Start with checking both sides of fuse holder. Use a needle if necessary to reach into the back side of fuse holder or connectors to read voltage if volt meter probe is too fat to reach in.
Next put one probe on head fin, other on battery
- negative. You should have power. This tests ground from battery
Visually examine every last inch of wire you can possibly see. Wiggle & tug on any connectors to check for loose connection. The metal tube inside the snap connectors can/will split lengthwise leaving only the tension of old hard rubber to hold bullet connectors it.
Next move to ignition switch & check that you have constant power at one terminal & then power comes out other terminal with key on.
We'll go from there.
Good thing is the fault is constant at this time so you should be able to pin point exact problem.