Small Engines (Lawn Mowers, etc.): 19hp Kawasaki stalling problem, ohv engine, valve adjustment

Question
I have a Scag w/19hp Kawasaki with a stalling/sputtering issue. When this issue started last year I could mow and it would mow fine for a while and then it would start sputtering at no specific time. It has 90hrs and I have replaced the coils (under advisment by the local shop) last summer and mowed a couple of times and it ran better than ever, but before I put it up for the winter it started the missing problem again. Now I tried to mow with it for the first time this year and it runs fine until you ingage the blades and it starts sputtering and running very rough like it did before replaced the coils maybe a little worse. How should I troubleshoot this issue? And what are the possible causes of this?

Answer
You may have a fuel delivery problem if it only happens under a load.  This could be carburetor or fuel pump, if it has a pump, related.  Possibly it could stand to have a valve adjustment.

Personally I'd do a complete maintenance which would include rebuilding the carb and adjusting the valves if it's an OHV engine.