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Sounds like a carburetor issue. The idle jet may be clogged. I would take it apart and do a good cleaning and blow out the jets with air etc..
Probably too much slack in your throttle cable tension. Adjust and tighten it up. Too much slack causes the ETC mechanism to think it is in a stuck throttle condition and will cause the contacts to be made which will kill ignition. Had the same issue on my 2008 Sportsman 500 EFI and I solved my dying out issue.Adjust up at the point where the cable goes into the thumb lever housing on the handlebar.