Sounds like a fuel starvation issue, so, first thing ya wanna do is enter your info here :http://www.kohlerengines.com/manuals/landing.htm
and check out the carb section. Could be the fuel shut-off solenoid acting up, if yer too cheap to buy a new one, just cut the tip off the plunger. It will work fine, just let it idle/cool down for a bit before shutting it off. If not that, then you need to get into the carb again and clean it out. Pay attention to the float level/ inlet needle. Could be sticking.