is it leaking through the top of the valve or from a cut at the bottom of the stem? Although this is a Presta valve, the parts are analogous to Schrader valves although the Schrader valve is clad in rubber. The green arrow points to the core. Core leakage is very rare on either Presta or Schrader. It is also something that is easily fixed.

The red arrow points to the stem. Stems being cut during inflation is very common problem and is due to user error the vast majority of the time. You can cut the stem if the rim has a burr but those are rare. More often, the user pulls on the stem while pumping and cuts the rubber around the bottom of the stem on a Schrader valve. If you are using a hand pump that you pump at 90° to the stem, you are much more likely to cut the stem than if you are using a pump with a hose where the movement of pumping is directed into the ground. If your problem is due to cut stems (more likely than a core failure), you want to reassess the way your pump the tire while on the road.