kohler k241 problem

Sounds like it's starving for fuel at mid to high speed which narrows it down to the carb.
The carb could be loose, the mounting gasket bad & leaking or something internal to the carb is failing.
In the carb the high speed jet could be clogged and/or partially clogged. The proper default setting for the high speed jet is approx 1.5 to 2 turns out.
You could try to turn it all the way in, counting how many turns it takes to bottom out. DO NOT run it down tight, just run it down until it bottoms out, then turn it out 1.5 turns then try it. If it doesn't improve, turn it out another 1/2 turn to equal 2 turns out then try it. If it doesn't improve it may be the following:
The fuel and/or ambient air passages in the carb could be clogged.
The float could be bad and/or the needle valve sticking not allowing enough fuel into the bowl which would starve an engine of fuel at higher rpm.
Any and all of the above means that basically a carb rebuild sounds inorder.
Good luck
Dave

I know this thread is over a year old, but did you ever figure out what the problem was? I had a similar problem with a Kohler K301, and it ended up being the battery. I cleaned the carb, set the needles properly, cleaned the points, etc. The engine would start and idle all day long. When I would increase the throttle, the engine would die. While the engine had a bad rectifier, I charged the battery, started the engine, and the engine ran like a champ.