My Coleman lantern pump cup has lost its shape, its not leather its rubber, Coleman calls it Neoprene. Half the time when I go to use it I have to take the pump out, push out on the Cup sides so it will catch when I pump. I guess thru the years the cup wall/sides have lost its form/shape.
Here is what I did to fix it, so far no problems.... Take the rubber or Neoprene Pump Cup off the pump, take a hard bowl with a flat bottom. Boil some water, wet and press the cup onto the flat part of the bowl. Suction will hold it spread wide open, then pour the hot water in the bowl. When water cools down the cup sidewalls will be flared out. When you put it back together make sure all water is wiped off. When you pump, the cup sides will now catch and pump air into the tank.
If you are having this problem, first add a couple drops of oil to the pump before you do this. Sometimes the cup gets dry and all it needs is oil. But if that does not help then maybe do what i did. Or just buy a new cup or pump assembly
