Greg,
Along with Roland's suggestions, check to make sure the wires are making good contact with a bright, clean, oil-free connection.
Since at some time you're going to need to change the spark plug anyway, check to make sure it is good by using a new one. If there's no difference, you still have a new replacement plug you can keep or use in another Cub Cadet. If you don't have another one yet, don't worry. You will.
The spark plug wire and connections can also corrode, crack, and break down, so check to make sure it is good with an ohm meter, or by substituting one you know is good. Sorry I don't have the Kohler specs handy, but typically plug wires should have 10 - 15 K ohms per foot. If somebody has specs available, I'll welcome the exact figures in a correction. The connection inside the coil end can corrode, clean it with a wire "bottle brush" (preferable) or rolled up piece of sandpaper/emery cloth and blow it out. Do the same thing on the spark plug end of the plug wire to remove any corrosion there. Brush any corrosion from the exposed male connections of the plug and plug wire. Make sure each connection is tight.
The coil itself can break down from vibration, heat, or cantankerousness. Again, I don't have specs right now, but I believe they are listed in the Kohler manual, which you can download for free. The procedure should also be included for checking both the primary and secondary windings of the coil.
If you check each component and connection one step at a time, you'll be able to pinpoint the problem.