When I purchased my SP it dit the same thing the mechanic knew exactly what it was. He took off the seat and repositioned the breather snorkel, it was against the gas tank starving it for air. Hope this helps.

 

Another possibility is the bolts that hold the carb to the head may be loose

 

If you are using a key chain on your key, it could be hitting the gas cap and turning it off. Also sometimes it will only turn it part ways so that the engine runs, but the spedo and electric cooling fan do not. Remember no key chain on a Sportsman 500!!!!