There isn't much to go on in that description, Aldo. I'd begin with three possibilities that are easy to deal with.
First, tappet clearance just about always decreases when the engine warms up, due to metal expansion at high temperatures. That is the main reason to have tappet clearance in the first place. Since the engine stopped when it got warmed up, there is a fair chance it was holding the valves slightly open, at those highly inadequate clearances.
Second, have you removed the cowls and checked that the air intake passages and cooling fins are clear, and the flywheel has all its fins? Poor cooling air circulation is prone to causing the fuel to boil in the carburetor, whereupon the fire goes out in the engine due to lean mixture.
Third, have you checked the rate of flow of fuel into the carburetor? You can get upstream problems that cause the fuel flow to stop after a while - in particular, blocked vent in the fuel tank cap, or a floating mass of grunge in the tank or outlet pipe that moves down the pipe when fuel flows, but goes back up when the engine is stopped. By checking that fuel flows full stream out of the needle-and-seat when you remove the float bowl, and keeps on flowing while you empty the tank through the needle-and-seat, you can check for that problem.
There are other things it could be, in particular high temperature breakdown of the ignition system, but there we get into stuff that is more difficult to test for, and way more expensive to fix. Would you mind checking those three things, making another test on the engine's behaviour after a long run under load, and reporting back please?
