Pump won't pump up tyre

Hi, I have a Dahon folding bike with a pump built into the seat post, which is very handy, but about six months ago the pump developed an annoying problem - whenever I try to pump up a flat tyre, the valve seems to get stuck 'open', and once I've pressed the pump down, if I let go it just shoots back up, meaning the valve isn't closing, and the air is just going into the tyre and then straight back into the pump as I pull it back up. (Or rather, as the air pushes it back up.)

I've checked the connector on the end of the pump, it looks fine, I've measured the distance that the black plastic 'cross' thing is in, from the end of the connector, and it's exactly the same as my other, hand pump, which works fine (about three to four mm).

Does anybody know how to fix this problem? I presume it must be something to do with the connector on the pump, because it used to work fine when I first got the bike about two years go, and my other pump works fine.

I've looked up the pump on Google and it's a ZorinPump, you can see a picture of it here:

http://www.zorinpump.com/zorinpump.htm

I have a Schrader valve, so don't use the Schrader to Presta adaptor which you see in most of the pictures on that site.

Just to clarify, I took apart the connector on my hand pump (which works fine), and inside there is a black cross shaped piece of plastic, and behind it a ball bearing.

In the ZorinPump connector, there is the same black cross shaped piece of plastic, but behind it there is nothing, just the hole where the air comes out of the pump tube. But there is a concave section around the hole, which looks like it could have had a ball bearing there. But the Zorin Pump used to work, but now doesn't, and I've never taken the connector apart before, so where could the ball bearing have gone, or did it never have one?

I realise now how the Schrader connector works: the black cross shaped piece of plastic pushes the valve in the inner tube open, as you screw the connector on, then the air pressure released by the inner tube pushes the ball bearing into the hole and stops any air from getting out of the inner tube. As you push down on the pump, the ball bearing is pushed forwards and the air goes into the inner tube, when you reach the bottom of the pump stroke, the air in the inner tube pushes the ball bearing back into the hole and no air can escape.

(I used to think that the act of pushing down the pump opened the valve in the inner tube through air pressure alone, I didn't realise the valve was open all the time.)

Does anybody have a ZorinPump that they can prise the black piece of plastic out of, to see if there is a ball bearing behind it?

I've searched all over Google for a single explanation of how the Schrader connector works, but I can't find one, which I think is odd, seeing as there must be hundreds of millions of them around.