Just a shot in the dark here, but are you losing fuel out of the overflow when it's not running?...if that's the case, you probably just need a new float valve. What happens over time, is the tip on the float valve gets worn and doesn't "seat" correctly, causing fuel to continue to flow.
Part # for a new float valve is....16030-1057...that's for an OEM.
My Kawie dealer has them listed for $34.13...but you should be able to find one a little cheaper if you shop around.