With symptoms like those, you can throw parts at it until you run out of parts to throw.
When it "dies", does it shut right off like someone turned off the key, or sputters like you ran the tank dry?
Pull the park plugs and describe what they look like. They often tell you the story.
As soon as it dies, check to see if you have a decent spark by having an acquaintance hold the removed spark plug against a good ground while you engage the starter. This will let you know if the problem is electrical.
