had the same problem with my sportsman 400. It did exactly how you explained it.  I bought the starter kit for around $40 from the polaris dealer and now it works great.

  I am wondering what happens to your quad when the coil pulsar goes bad?  My bike shuts down when im driving, but when I wait like 20min, it cools down then I could start it back up. The bike might go for a whole day without shutting down, or it might go for a few hours/minutes and shut down  So, I was wondering if it was the coil pulsar. If not what else could be the problem?

Problem solved