THIS MAY SOUND WAY TO SIMPLE BUT I HAD THE EXACT SAME PROBLE TO A TEE AND BELIEVE IT OR NOT THE BATTERY CABLE WAS LOOSE WORTH A TRY HOPE IT WORKS OUT FOR YA

 

one more thing i just remembered check the throttle body to make sure it is seated into the motor correctly this can be really hard to notice and will for sure cause problems what caused mine to do it was a backfire please let me know if that was it good luck

 

welp just got my 500 back from the shop after having the same exact symtoms as you.

they performed a diog. test on it. app one of the wires that come off the sciloniod was shorting out. when it shorted out my whole system would shut down. and of course it would fire back up and cut back off when the wire decided to short itself out. kinda makes sense i guess.

so they ran new wires and 98 bucks later i guess swhes healthy again. let u know for sure this wknd. check your silinoid!!