Really sounds like a similar situation I had once. Ran perfect when first started, then after about 10 minutes die and could not restart, then after 15 minutes it would restart. Finally found that I had some foreign matter (looked like a pieces of paper towel) in the tank. It would come dislodged as the engine ran and float around until it got sucked up on the dip tube, which would cutoff the flow of fuel. After it dies, reach into the fuel tank and feel to the right, you will feel the dip tube going down, see I anything is stuck to the bottom.