[Deadhead]

Take a flashlight, look down in where the washer/stem thread in & check the seats. Could be that they are all pitted up or corroded. This will make you go through washers like crazy. You can replace them really cheap. You need a seat wrench to get them out. Not too expensive either. A BIG allen type wrench with square instead of hex end on it. Wrap it sharply with stout metal instrument to loosen seat, take to real plumbing supply store to find correct one & replace.