I worked on an 06 500 that had a similar problem. It would run good for a few minutes and then start bogging down under half to full throttle and for a few seconds would run good. After doing a tune up and changing the fuel filter and getting nowhere, i noticed if i turned it off for as little as 30 seconds it would run good again for a few minutes and then i decided it was the fuel pump getting hot and not making enough pressure. I swapped the pump out and it hasn't missed a lick since. Not sure this is the same problem you have but definately worth checking into.
02 Sportsman 700 custom bumpers & 27" 589s
01 Sportsman 500 HO Ducks Unlimited Edition