One thing you might want to look at is your fuel tank cap. The problem you describe can be caused by it not venting correctly. Is there fuel visible in your fuel line between the tank and carburetor?
I've also heard of CDI failure that can cause the same condition. It has been reported several times that after a cool down period the CDI performs correctly then overheats and the ignition goes away.
Check for the venting problem by leaving the fuel cap loose and see if the engine dies.
If you have a spare, switch the CDI with a known good one. Try one thing at a time.
Get back to us with what you find. Good luck.
Tom