Small Engines (Lawn Mowers, etc.): Craftsman Self-Propelled Lawnmower, self propelled lawnmower, inductive timing light

Question
I am trying to get this mower running for my widowed neighbor.  She already had the plug,  filter, blade and oil replaced but it won't stay running for more than a couple of seconds.  One place told her it had a shot engine.  I cannot believe this as it sounds fine when it cranks and it doesn't smoke or clatter or anything like that.  It sounds more like it just turns off--no sputter, choke, etc.  I keep thinking it might be the float in the carburetor or somehting like that.  The model number is 917.377.580.  Any suggestions?  

Answer
The first thing I'd try is loosening the fuel cap.  The symptoms you describe can be caused by the fuel cap not properly venting the tank and allowing sufficient fuel flow to keep the float bowl full.  If this helps, replace the fuel cap.  The next thing that could be an issue is ignition.  If the ignition module has a problem related to heat, it can often produce spark for a while and quit when it gets hot.  You can verify this with an inductive timing light to see if the spark quits suddenly.  Another issue could be a problem with a burnt exhaust valve but that usually makes an engine hard to start as well so I don't think it's the problem (but something to consider if the first two things I mentioned aren't the problem).  Another thing could be the carb needs to be cleaned thoroughly as indicated by the engine only running after being primed or while on choke.  You didn't mention this but in the spring, old fuel gumming up the carb is the #1 problem with seasonal equipment.  Hope this helps.