If it hasn't been serviced in awhile, I would start with points, condensor, spark plug and see what happens. If you let the key on without the engine running and the points happen to be closed, the condensor can burn up and cause the symptom your describing. I had a 140 with a Kohler do that once.
If that doesn't work, please let me know if you have done any other work to it or if working the choke will keep it running a bit longer before it dies.