[oldE]

When the engine stops while releasing the clutch in neutral, does the car lurch or shudder as if the engine was being overcome by load or is it stopping as if switched off?
Wild guesses:
If it is lurching to a stop, I suspect you might be getting a 'false neutral', however, since you can push the vehicle in neutral, that doesn't seem likely.
If stopping as if it were switched off, I would look closely at the wire related to the circuit which prevents the car from being started without the clutch being depressed. It might be causing something else to short and interrupt either fuel delivery or spark.

Best of luck.
Les