Once it runs out of fuel, how do you restart it? How long does it set?
I would bet that a new carb will do the same thing. The float is the controlling factor in the fuel delivery. If it sticks, they flood out or go dry, and either one will happen pretty quick if you are driving. I can't see it happening over time and fixing itself.
Are you sure its not icing up? 30 minutes would be about right to form a good layer of ice down in the venturi.
If you go with a replacement carb, stick with what the factory used.
Joe
