I'm not sure why you say the carburetor is not the problem, but if it's not, then you have a few other possibilities.
First it culd be a problem with the ignition system. When they get hot, they sometimes start to break down. Usually the either start to miss a little , but then they usually stop altogether. You may have one cylinder that is working ok but the other one may not be running correctly or a t all.
Next it could be a problem with the gas cap. If the vent in the cap is not venting, then this could be a cause of the engine trouble. Loosen or remove the fuel cap and see if it clears up.
Next you vould be the victim of "Vapor Lock" This happens especially in hot or humid weather.
You have several possibilities.
Just read all of my answer before you act.
1. Todays gasoline is not the same as it was just a few years ago. There have boon changes in gas formulas. DO NOT USE REGULAR 87 OCTANE GAS! Use a good quality, good brand 89 octane fuel. DO NOT USE CHEAP GAS.
2. One of the problems you seem to have is a phonomenon called "VAPOR Lock".
This is caused when fuel vaporizes in the fuel line and doesn't allow the proper amount of gas to get to the carburetor. This is usually caused bu the fuel ine getting too close to a heat source such as the muffler of the cylinder head or even sometimes the engine block. Also cheap fule of 87 octane fuels will cause this to happen more often. Check all the fuel lines and make sure that they are away from heat.
As mowers are operated, they tend to accumulate grass under the engine shoud. We call this a "Birds nest or mouse nest." These nests will keep the engine from cooling as they block the flow of air to the head and cylinder. Clean this grass out several times a year.
3. Another issue can be a fuel issue in the carburetor.
As engines sit or get older, fuel that is left in the carburetor can turn to gum and varnish and cause this and other problems.
Also, any gasoline that was left in a gas can for a period of more than 30 days must be discarded because it also has begun to turn to varnish.
More than 70% of all of our repairs in our lawn mower business are due to this same issue. You most likely have dirt, gum, varnish...etc in your carburetor plugging up the small passageways and jets in the carb. It Must be removed from the engine, cleaned very well, blown out with compressed air and reassembled using a NEW carburetor rebuild kit. ALWAYS clean the fuel tank and replace the fuel line when doing this repair or you may have to do it all over again. The inside of the fuel line disintegrates over time and these small pieces of rubber will plug up the carb too. Dirt and water from a dirty fuel tank will also plug up the carb. Find the Model, type and serial or code numbers off of the engine and take them to your local dealer to get the carb kit.
4. Make sure that you install a new Air Filter. DO NOT CLEAN AIR FILTERS always REPLACE. Replace air filters no less often than every 20 hrs of use. Plugged air filters will cause many problems.
There may be other things, but this should be enough for now.
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