I have a 19 HP Kawasaki engine on a Scag mower. The mower has two fuel tanks feeding a select switch then passing through a fuel filter to the fuel pump.
When under power, the fuel engine intermittently misses for a duration of a couple of seconds to 5 to 10 seconds and normally recovers for a short period only to repeat the symptoms.
I have replaced the fuel filter, the fuel pump, air filter, (oil looks good), bypassed the fuel switch, and insured the vents in the two fuel caps are breathing. I have also bypassed the fuel switch and fed the fuel directly from the tank to the filter to insure the switch was not a problem.
I have observed the fuel filter to appear virtually empty of fuel (filter has clear housing) when the engine is missing but cannot determine the cause. I have drained the fuel from the bottom of the carburetor and there appears to be no water in the fuel. I have used carburetor cleaner and currently have Sea Foam in the fuel tank to help remove any lacquer although living in Florida, the mower has never set for any lengthy period of time.
I have been reluctant to adjust the carburetor since when the engine is not having a missing spell, it runs strong.
Open for any suggestion of what to try next.

It sounds as if you may be dropping a cylinder when the load is applied. You might want to check and adjust the valves on both cylinders and see if there is any difference. It may also be one of the ignition modules starting to break down and loose spark to one of the cylinders.

http://www.mymowerparts.com/pdf/Kawasaki_Service_and_Repair_Manuals/FH451V%20FH200V%20FH531V%20FH601V%20FH641V%20FH680 V%20FH680V%20FH721V%20%2099924204503.pdf

Thank you for the suggestions and the repair manual. I will follow your advice and let you know what I find out.