There are several possibilities: 1) The fuel pump is failing as it gets hot - you can verify this by squeezing the primer bulb while trying to start the motor. If it starts, you have a fuel pump or fuel supply program. 2) The fuel pump is sucking air when the hoses get warm - check all hose connections. 3) The engine is overheating - gently touch the head - if it is hot enough to cook eggs, then it's overheating. 4) There is a short or open circuit that occurs when the engine warms up enough to cause expansion. Favorite places for this to occur are the kill button, magneto connections, cracks in the coils, too much grease around the mag plate. start with the kill switch and then inspect the coils for discoloration or cracks.
It is probably not the condensors - capacitors are generally on or off, once they fail, they stop working entirely.