Why is my 2004 polaris predator 500 shutting of while riding it

It is a known issue. Check out the link.

https://www.google.com/search?q=2003+polaris+predator+500+wont+start

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what year is it ?

1. Place the transmission in first gear

2. Rotate the lockout switch forward to unlock reverse gear

3. Shift into reverse gear

When you shift back out of reverse gear, the lockout switch will reengage automatically to prevent accidental shifting into reverse

Yes you do or just go to the store that you bought it or return it to the person that you bought it from. Thanks for my option

Maybe, vapor lock. Gas cap is not venting.

Thats not much info but ck the fuel supply and or coil.

get it serviced now, its very dangerous.
and do not park it , INDOORS.

Semi-synthetic 0w40 oil for the 500,600,700 sportsman quads, check what clutch your ATV has, "cvt" (continuosly variable transmission) clutches, or 'wet clutch'. 10w-40 or the 0w-40 that has the additves for "wet clutch" aplications

have you checked the valve clearances?

having same prob with my preditor 500 any advice