This will not be anything new, but whenever I approach an engine problem, I try to narrow it down to one of three categories: Spark, Fuel, or Compression. That being said, I doubt your problem is compression since it runs for awhile to begin with... This leaves fuel or spark, so I agree, after it dies the next time, check the spark. Check the fuel lines to ensure that there is not a blockage. If the lines are restricted, the motor will run until the bowl empties, then no more fuel until the bowl is refilled, and if the lines are blocked it could take a little while. The petcock is easy to take out, and doing so allows you to inspect the pick-up screens from the fuel tank.
Once you've narrowed it down to one of those three categories, problems are a lot easier to deal with.