Small Engine Troubleshooting Problems? Ask a Mechanic Now.
run a cylinder test. Loosen the spark plug wires, then with engine idling, remove one wire at a time. If engine dies when one is removed, the opposite cylinder is not firing.
You may have to do it after it warms and is acting up!
With Kohler twin, likely one of the ignition module /coils. is cutting out when hot.
If that is the case, Kohler recommends replacing both at same time.