Starter Limits...
I've been on the aircraft 9 years and to my knowledge there is no limit on the starter and none in the books. Maybe the mtce manual has one but there is nothing in the limitations section either. And yes, Autostart will attempt 3 starts and shuts down. If you're still having a problem after a 3 start attempt, then there is something wrong.
Takeoff power is limited to 5 minutes but can be extended by the manufacturer to 10.
Hope it helps.