I have a 3.5HP Tecumseh engine on a Sears edger. Starts 1st pull runs for about a minute and dies. Still has spark and fuel but will not restart. I've cleaned the carburetor, cleaned the coil and flywheel magnets. I'm baffled. It's like something gets warm and quits, but I checked for fire and still have it.

You are seeing spark at the plug, grounded to the head when it's acting up??
 
Can you check the compression?  Perhaps a valve isn't closing fully once warm...
 
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