I'm not familiar with that new of a model. In earlier diesel models, once the engine is started the only way to shut it off was to pull out the handle that kills the engine, as that is the only way to stop the flow of fuel to the injector pump, and there is nothing electrical required to keep that style of engine running once it has been started.
Does yours normally turn off when you turn the key off, or does it have a separate kill handle that yu pull like the earlier ones?
If it turns off with the key that means that there is an electrically controlled solenoid valve that stops the fuel flow to kill the engine, and I would be looking there, most likely the wire from the "Run" position on the key switch isn't getting voltage to the solenoid or the key switch itself has gone bad.

If it has the earlier style handle that you pull to kill the engine then the key switch should normally have nothing to do with killing the engine once the engine has started. The only thing I can think of might be that the bendix on the starter is stuck with the starter gear always engaged with the ring gear, and so when you let the key drop back from "Start" to "Run" the drag of the starter on the engine causes it to die, but that is only a guess.