Assuming we're talking about the little Bing carb, with the round float bowl that screws onto the carb body..
The gasket is there to prevent sloshing gas from leaking out around the edges of the bowl-body connection. It should have no real effect on running, if it were missing . The float bowl is vented to the atmosphere already, via the bowl vent passage.
But you mention that the float bowl runs out of gas. That sounds like a fuel supply problem - plugged fuel valve, filter(s), lines etc. Possibly an issue with the fuel inlet needle & seat. Doubt that the gasket is playing any role in this, but I would replace it anyway, as it is there for a reason.