if you have a condensor on your engine, it 's possible that once the failing condensor gets hot, it shorts to ground, thus preventing spark until it cools down. The condensor is a small silver can that's part of the ignition system.
im tellin ya either clean or buy a new carb it will run fine also is it a craftsman because their yard equipment is usually garbage but their tools r good but anyway i was working on 1 the other day and it had a plastic carburater which is sad
usually those small engines have plastic carb's to make the engine less expensive so it would be nothing to replace them. i had asked one time about replacing an all metal one on a riding mower no resemblance but it was about $190.00 thats why there plastic on those small ones. as for craftsmen mowers yeah there cheap but they have a fix it or replace it warrenty so if replacing the carb doesn't do it get it checked out