On cutoff saws it is absolutely critical that the air filter seals 100% perfectly,if the motor ingests any concrete dust ot metal dust the cylinder and piston will wear out extremely quickly. On cutoff saws check the piston intake skirt(pull off the carb and look with a light) if you see any scratches at all pull off the cylinder and check the nikasil plating below the intake port,it can be worn away to the aluminum. Ingesting abrasive particles is what kills most cutoff saws.
All sealing surfaces of the air filters should be sealed with a thick heavy grease like wheel bearing grease.
Like the other guys said,if it's quitting when hot it could be the ignition or a bad tank vent. Just replace the vent to eliminate that possibility. Also when it quits immediately check it for spark.