Valve cores are cheap, just replace it. I've had them fail due to trash so keep a valve cap on them. Also due to oil contamination causing the rubber or plastic on the valve to swell and stick. Many years ago there was a brand of imported tube that had zinc stems instead of brass. They tended to build up a little corrosion inside the stem. There used to be both short and long Schrader valve cores...I always had the best luck with the short ones. Also they used to make many Schrader valve cores out of brass but I have always preferred the stainless steel.