Whenever I have this type of problem, The first thing I try to do is pull a spark plug or 2 as soon as the engine dies and look for either bone dry or soaked with gas condition.
Bone dry will indicate fuel delivery issue upstream of the carburetor, or the float needle is nearly glued to the seat, greatly reducing fuel flow into the bowl.
Wet spark plugs would indicate a carburetor problem, causing a flooding condition.
