Small Engine Troubleshooting Problems? Ask a Mechanic Now.
Welcome to JUST ANSWER small engines, let me try to help you !! I don't know it all, but maybe together we can get you a satisfactory answer!
See link above. # 22 is the anti-backfire solenoid, that plugs the main jet in the carburetor when it is closed. It may be getting hot and dropping out. Best test is to remove it and plug the hole and run test. Or listen for the click of the solenid when cold, by flipping the key on and off. Learn what it sounds like, then when the mower quits, flip the key on and off, listening for the click. If it does not click, the fuel will not get to the cylinders. Whit twin Kawasaki engine, not likely it is losing spark, much more like lt it is loosing fuel.