RHD,
You've got to get your gate voltage, and load current on a scope to check things out.
Even something like a cheap switch that "switches" poorly can allow sloppy and damaging di/dt into the gate.
Do you have a picture of your setup?
My first guess could be that there is possible (but not necessarily probable) damage to the gate during the turn on transient. Try adding a 100 ohm resistor in series with the gate.
The circuit you copied demonstrates well, the voltages that need to be present for a small, basic switched load. But it does not take into account other physical processes that can take place when your load is more complicated.
For instance, a (cheap) switching circuit is more likely to have noise - everywhere on it. Even on its 'GND" terminal - especially if there is a poor connection from the circuit to GND. Its GND node could be sitting at an unstable voltage directly affected by the switching noise. Let's say this is happening - severely. One could add a bypass capacitor across the drain and the source in an attempt to make the load look more like a smooth and stable DC load with no AC quirks about it.
But that is just one example. If a switching circuit is killing things off, there could be some inductive feedback getting back to your FETs drain somehow.. it would depend on the topology of the switching circuit of course.
For now, try adding a series resistor on the gate, a rectifying diode in series with your load and the drain, and a capacitor in parallel with your FET. Just see what happens. Sometimes you just have to continue with additional experiments.
Honestly though, I would be surprised if that helps at all. I'll go back to what I said initially. What would help most quickly is a nice set of startup and shutdown transients, as well as some steady state current measurements all about if possible. Some pictures of your experimental setup is also a bonus.