Small Engines (Lawn Mowers, etc.): Craftsman mower starts but does not continue to run., blown head gasket, new spark

Question
My 8 year old Craftsman self propelled push mower has been in and out of 3 different small engine repair shops in the last year, all for the same problem.  The engine will start but shuts off as soon as the gas pumped into the carb. by priming is used up.  I prime it again and it runs just until that gas is used up and the cycle continues.  Everytime I take it to a shop, they clean the carb. or the air filter, hand me a bill and it runs fine for the first two mowings then it goes back to the same problem.  I finally took the carb. apart myself, cleaned it (with some help), put in a new spark plug, new gas, new oil and it started up and ran fine for two mowings, now it is back to the same old thing.  Surely I am not getting dirt in the carburator that easily?  A friend suggested the govener (spelling?) may be the problem.  Any thoughts or perhaps use it for target pratice?  I have noticed several of the same questions concerning the same problem on this site.  Could this be a Craftsman defect?  

Answer
Linda, It just may be a "hung valve" or a "blown Head Gasket". Suggest that the head be removed right after it quits and see if the valves are closeing properly as well as ck the head gasket....Next time a "shop" repaires it, have them test it in front of you........Bob