I will tell my story as some of you have described similar troubles, I purchased this CC LT 1045 with 42" cut, used, last spring. A month of use and the Kohler courage 20 Hp started losing power and sputtering and then backfiring. It would always restart and run until put under load. I,read of several similar problems on here, talked with a small engine mechanic and started some actions. 1st, changed fuel filter, no help. checked vent on gas cap, changed gas, blew out fuel line, no help.
I noticed that oil filter was an inexpensive brand and assumed the oil was also(changed before I bought so it looked clean). I drained oil, installed Amsoil 4 stroke small engine oil, put on a new Napa oil filter. Added Amsoil "Quickshot" to gas. It took a month to get to running better. At first it would go a short time and die again. The time started getting longer each time. Now, after about 2 months it seems to run normal. I mow approx 2 to 3 acres and it will do 2 to 3 hours and not fail now. My thinking is that it had to do with hyd lifters being gummed up and not functioning, and the hi tbn oil and varnish cleansing product slowly cleaned the engine so it could work normal. It would have been very costly to have a mechanic tear down to repair or replace hydraulic lifters or what else he would find, so I am happy!.