If there is an obstruction in the exhaust, you can often hear a hissing or whistle out of the tail pipe for a few seconds after you shut the engine off. Also check your carb preheat flapper valve in the exhaust manifold to see if it is stuck closed.
Check to see if you are building pressure in your exhaust system. If you have a blockage somewhere it causes wierd problems like the ones you describe, however it will usually start first and then die.