I have a 2001 500 HO. After I crank it and ride for about 20 minutes, it will just die out like someone shut the gas off. Try to recrank the bike and it backfires some and will eventually crank to an idle only. Don't give gas or it will die again and probably backfire while trying to crank. Let bike sit and cool for a while and I can go out and ride, but after 20 to 30 minutes it all repeats. I went through the fuel system and have not really found any problems. I've pulled hoses and tubes and sprayed the carb with carb cleaner while still on bike. Besides pulling the carb, I'm not sure where to go from here. If possible maybe someone out there could give me some ideas.

 

check the gas tank vent hose

 

Yes check the vent hose, just loosen the cap and see if it does it again. if it does than i would check the spark when it dies. You could be getting a weak spark after it heats up>