I agree this might be your issue. If you look carefully at the presta valve stem, there's a threaded portion right below where the little nut you unscrew to put air in is located; that's where the valve cap that came with the tube screwed on. Then immediately under that little threaded portion is a smaller diameter smooth bit, and under that is a larger diameter part that may be threaded or not (threaded ones usually come with a nut that you can use to secure the valve to the rim).

The pump chuck/head should have an o-ring that locks onto the little smooth area to form a seal. If you have the threaded valve stem and push it on too far, it tries to seal on the threads but air can just run out through the threads since you can't form a tight seal on the threads unless you seriously deform the o-ring. And even if you do, you've chewed up the o-ring so that next time it's even more likely to leak.

Also, a presta valve only stays closed because the pressure inside the tube forces the valve shut against the lower air pressure outside. So if you push the chuck on too far such that it's pushing the little threaded pin with the nut, the valve will be stuck open while you're trying to fill the tube with air.