Does the starter motor continue to run after the engine starts? If the engine doesn't fire, it's possible for the load of cranking the engine on the pinion gear to keep the gears engaged, and also keep the solenoid contacts closed, even if the voltage to the solenoid is removed by turning the ignition off. Tune the engine so it starts quickly and unloads the drive gear, and the problem will disappear. I've encountered the problem several times, and making the engine start reliably always makes it go away.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!