I looked up what the overlays are made of and found that they are made of “silicone rubber with a silicone top-coating for a smooth feel”.
So it’s the silicone top-coating that is wearing off and thus - loosing that smooth feel.
The silicone top-coating is wearing off because my fingernails are making contact with the coating when I play. My hands are clean, don’t wear lotions and my fingernails are kept relatively short, but it is difficult to avoid fingernail contact when your fingertips come straight down on the keys. I don’t scrape my fingernails across the surface, but they do touch frequently. Also, finger oils are unavoidable and wonder if that would break down of the top coating.
I think that any new overlay’s top coating is going to wear off from normal play, sooner or later, so I’m going to figure out how to restore the coating myself. I will start by looking for a silicone coating that can be sprayed or rubbed onto the keyboard.