Kawasaki FH661V engine dies

My neighbor has a JD X360 with this engine.  It dies in 20 minutes when it's hot out.  Longer when it's cool.  After it's cooled off it starts right up again.  The coils, fuel pump and carb have been changed and didn't fix the problem.  I don't see an ignition module anywhere.  Is the solid state circuit inside the coils?  We're stumped.  I do have a new voltage regulator I can put on it, but can't see how that would be the problem.