Follow the fuel line all the way back to the tank as sometimes soft spots are localized and simply collapse- especially if this is a pump model. Valves .003 / .005 cold 1/4" PTDC?

IF tomplum's suggestion doesn't catch it, check if there is good compression when engine shuts off. Valve may be sticking OR valve seat may be loose. Also check the fuel solenoid is open, may be short or bad connection dropping the carb solenoid out OR carb solenoid may be failing (doubt that is it)

AND you need to see if it has good spark when it shuts off.

Walt Conner