Kohler power loss
Look thru this site for posts on Kohler. There are a lot of reasons why Kohler 25's will lose power. Your engine will run fine with the fuel filter showing very little fuel inside. Try to see if you are running on 2 cylinders when it fails. If not a failing coil is possibly the reason for the lack of power. Usually this will show up in the first 200 hrs of the engine life. Otherwise you may be losing compression due to a loose valve seat or loose valve guide.
To find out if the problem is a non venting gas cap, loosen it when the unit gets hot and begins to cut out to test that theory.