there's no kick-in of the auto shutdown, something else must be going on. the auto-shutdown is not an automatic shutdown of the engine but of the electrical system to disconnect some feeds providing 12v during normal operation if the engine is not running - if it is not spinning the relay will disengage (not the other way around as in engaging when not spinning). once you crank it again it will re-engage.
like i said, something else is going on, maybe the same thing that makes you stall the engine is the reason is not starting afterwards.