The first thing I thought when you posted was that your pump head gasket is worn. I've never had a valve stick closed - any time I've had a valve core go bad, the tube won't hold air, not the other way around.
When you said the pump inflates your other tubes fine, I hesitated for a bit until I realized that one of the first things that happens when a gasket starts to go, is that it bends the top of the valve core by moving around on the stem during attachment and inflation. Once the top of the valve core is bent, it's extra hard to get the pump head aligned properly so that the valve will accept air.
How old is your pump head gasket? It's hard to compare ... but riding and pumping probably an average of three days a week for six or seven months out of the year, I got about four years out of my last one. Say 600 inflations or so. They're cheap anyway, half as much as a new tube costs and it will definitely save a lot of aggravation. I hadn't tracked my usage before, but I think I'm going to put my pump head gaskets on a regular replacement schedule.
Speed comes from what you put behind you. - Judi Ketteler