Small Engines (Lawn Mowers, etc.): Craftsman single stage snow thower, craftsman model, first snow of the year

Question
I have a 5 HP single stage craftsman snow blower this is its third season. The first snow of the year my blower will run great for 45 - 75 seconds and sputter and die.  I start it again with just the starter and it will run again for the same amount of time.  I have cleaned the carburetor and replace the fuel filter and no change. I do open the choke one notch when starting back up and then I need to adjust it back down immediately.  I have tried to feed the engine with the primer when it starts dieing but just runs rough until it dies, a quick pull and it will fire right back up again.

Answer
Have you tried replacing the spark plug.  I am assuming you have a two-cycle engine, is this correct?

What is the Craftsman model number?  The model number is located on the Sears sticker and is similar in format to xxx.xxxxxxx or xxx-xxxxxxx.

Let me know the model number so I can look up the carb.

Eric