That sounds like a Perry carb. Very good design at a time when many carbs were difficult to adjust and perform well. Does it look like the ones on this web page:

http://www.perrypumps.com/prod01.htm

There is a small volume inside the carb that holds fuel, so it can run for a while when the fuel is disrupted from the fuel tank. And I belive there is also an internal fuel filter, which can clog up with conjelled oil. So a careful cleaning may solve your problems. It also depends on an O-ring or two. It's been a very long time since I've had one apart.

There was an article on the care and cleaning in RCM if you can find it.

PERRY CARB METERING SLOT, CLEANING, FOR WHAT IT'S WORTH, Smith, Jerry, Dec-95, 84