Could be some unrepairable corrosion around the seat.

Probably not the answer you wanted, but I had the same thing in one of the units of one of my clients, and I bought a whole new fixture -- about $50, has the quarter turn ceramic valves. It's like Lexus compared to a beat up 30 year old Toyota.

The down side was getting one of the nipples out, needed to do that because one of them was corroded enough so that it wouldn't hold water once I put it all back together.

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Te futueo et caballum tuum

1986 300SDL, 362K
1984 300D, 138K