Just shuts off

[Unit 5302]

Since both your spark and fuel are affected you should be looking at parts that effect both systems.

That can throw the fuel pump relay, ignition module, stator, and tons of other parts out the window.

What you are left with is the ignition switch itself (mine went bad and the result was EXACTLY what you describe). Also the PCM itself, since it controls the fuel pump relay and the ignition. I'm not sure if the inertia switch controls ignition too, my experiance with that switch is, it's all or nothing. There is no intermittance involved. Since it merely completes a circuit, there is no reason for it to be intermittent.

I would put money on the ignition switch itself.

Good luck.