I have just been through this and wrote this up for others that may have the same problem
Cub Cadet Model 2146 Tractor
Statement of Problem: While mowing along the mower just quits. It will not start until it cools off. Then it will start again.
Steps to isolate problem. (while doing these checks keep the mower in the parked position with the parking lever engaged)
1. Pull the air filter off and observe the throat of the carburetor to check that gas is getting to the carburetor, you will probably see it as you crank, you will also get some vapor from the exhaust pipe. If that happens then it is probably not the fuel system. Even though that was evident I still changed the fuel filter and cleaned the bowl of the carburetor but it was not necessary.
2. After it has stopped, Pull the spark plug and with the coil wire on it and the base grounded crank it and see if you get any spark. I did not. I changed the spark plug and no difference(after it had stopped).
3. Again after it has stopped and won稚 start, take a meter and set up to check for continuity using the ohms measurement to ground. One lead on ground and one lead one the connector (9) in the drawing on page 26 of the manual on the yellow wire coming from the harness (you should easily be able to put your probe in the connector. With key in the stop position you will get a short to ground, switch the key to any other position and this should no longer be a short to ground. If you still have a ground then there is a problem with one of the safety switches or a wire shorted to ground. In my case the switch worked normally. To make sure this was the case I removed the pin the yellow wire was on in the connector and waited until it had cooled and started it up again and ran it and it still stopped. (if it does not stop then you must either pull the plug wire or reconnect the yellow wire while it is running and shut it off with the key or just jump the connector to ground) This would probably indicate an intermittent bad safety switch or bad wiring. In my situation, it still did stop once it heated up.
4. That leaves only one thing, the coil. It is had to measure a coil in a static mode, I have read that the coil can break down with time, and this particular article I read that it is though that a spark plug that still works but is requiring too much drain can cause this malfunction. I ordered a new coil, I replaced it and it fixed the problem I had been having. My out of pocket expense was for a new fuel filter, new spark plug and the coil itself. Oh, yea, I paid someone to mow my front yard twice while in diagnostic and repair mode. So my cost for this was about $200, my time was free. Not bad, I could have spent $3000 easily replacing a perfectly mechanically sound tractor/mower with only about 4000 hours of use.
I have also wrote a procedure to replace the coil.