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!
When it is acting up, run a cylinder test. Loosen the spark plugs and with it idling, remove one wire at a time and see if engine will continue to run, If engine dies when one wire is removed the opposite cylinder is not firing. Check it for spark, and if o spark you need te new coil. And with Kohler, they recommend replacing both coils at same time.
I see question is still open, did you get to check the cylinders?