Yep, Trask is right. Probably varnishing in the low speed passages of the carb. When you start to come down near idle, you "run out of gas" because of that. As long as the tank vent is open, you should be OK, but it's a good idea to check the fuel cock, pump, and filter just to be sure you have a good flow to the carb. I would prefer that the carb be cleaned without using any pointed objects if possible -- because it's easy to accidentally make seemingly insignificant scratches in the passages that end up making major disturbances in the flow of the air/fuel mix, wrecking the $110.00 carb. Spray carb cleaner is typically not aggressive enough to dissolve the varnishing, so real carb dip, sych as Tyme, available in 1-gal cans at the local auto parts supply store, is called for. After a complete disassembly of the carb (including removal of the jet and emulsion tube), a 4-hour soak at room temperature, followed by a blow-out with carb spray, then a careful reassembly should get your idle back. While you have the carb apart, also pay particular attention to the float valve needle and seat. You may have wear or damage to the viton seal that regulates fuel flow. If so, a carb kit is called for. Full info is in the factory service manual. You will want to know your precise model (probably NSF4A2) when ordering anything for it.