You've got 2 of the three essentials covered--air and spark. You likely have a fuel delivery problem--replace the intank fuel filter, check your fuel lines for any soft spots/air leaks. Have you checked your tank vent--you should be able to suck air through it--if the tank vent is not operating properly, you'll develop a vacuum in the tank that the carb cannot overcome when attempting to pump fuel.
Have you cleaned/removed the muffler screen?
Check for air leaks in the intake area. I've seen a few isoblocks develop cracks that expand after getting hot.
Just a couple of thoughts.
Other than the above, look at a carb rebuild although since you say it will run for 15 minutes, I doubt that the carb is the problem.