This is a tough one. Well, I guess you have break it down. It needs gas in the right ratio and a spark with the right timing to start. Probably simplest to start with the spark. Does it have a good spark at the sparkplug when it does this? There’s gadgets available that you insert in-line in the spark plug leads, which makes determining this easy to do. Harbor Freight sells one.
http://www.harborfreight.com/catalogsearch/result?q=spark+plug+tester