As per the attached photo and
web page, what he calls a 'compression valve' but which I call a 'valve seat', made of brass, keeps eroding across the 'face' of the valve, where the rubber gasket presses against to shut it off.
The same thing happened to me. You put in a brand new valve seat, and within half a year or a year, it erodes across the 'face' and a runnel or groove is formed, resulting in an unfixable leak. It does not matter if you use a 100% brass valve seat, or a nickel-plated one. They both erode.
How to fix. The 'fix' is simple to describe, but a little tricky to perform, but my 'fix' has been going strong for five or six years now with no sign of quitting.
Take a new valve seat, and rough up the 'facing' (where the rubber presses against the flat circle of the valve seat), using about 200 grit sandpaper. Don't try to reform it; just rough up the 'face'.
Next, take electrician's solder, and create a ring-shaped layer of solder on the surface of the valve 'face'.
This is the 'easy to describe, but tricky to do' part. I had to use a big old-fashioned electric soldering iron, mounted in a big bench vise, pointed straight up, to put the brass valve seat on and heat it up. Before you do that, you need to apply a thin layer of soldering acid paste to prevent a micro-thin layer of corrosion from forming when heated up, which would prevent the solder from bonding. At the same time, you want to avoid getting solder on the valve seat threads, which could interfere with screwing it back into place in the valve body. If you get it in the threads, just heat the entire valve seat up and drop it on the bench a few times to shock it physically and knock the excess molten solder off.
The really tricky part, is that, as you apply the solder to the valve 'face', there will be a persistent tendency for the solder to form a 'bump' on one part of the ring of the valve face, and a dip or dimple either next to it, or opposite it, on the ring of the face. I had this happen repeatedly. It was so persistent that it was positively mystifying. I tried getting an extra-thick buildup of solder and sanding it all down flat, and I kept wearing through the thin layer of solder and exposing tiny areas of brass on the valve face. Time and time again, over and over, and over and over, I ran into this problem. Finally, after about an hour, I succeeded in getting a uniform layer of solder on the ring of the valve face that was smooth and flat. Then, I had to do it to the other valve; because there are two valves; 'hot' and 'cold'.
I did this about five or six years ago, and I have not had to service the valves ever since. Just that tiny layer of solder, bonded to the brass valve seat. That's all I did. This has been the result.
edit: If you must, you can try to salvage and reface an old valve seat with a groove in it. Just rough it up, including the groove, and refill the groove at the same time as you reface the valve face. Come to think of it, that's what I did, but mine wasn't as bad as the one in the photo. I fixed the leak and it stayed fixed.