I'm having a similar issue, though mine and my wife's rings have this happening on the opposite direction to what I've seen in here thus far (in the direction of the rings' circumferences). Hers arrived with an edge to it there that grabs things, and mine developed an edge to it that now if I touch it it is obvious that the inlay will peel directly off the ring. I've stopped wearing it because of this and I'm rethinking purchasing the front door lock we were planning to get.

I was thinking about this and something I think I saw John say at one point was about 'keying', and keying the edge of the ring so that when the inlay is poured in it can fill a keyed slot around the perimeter would be the only way I could see these things staying put permanently. Maybe that kind of thing is too difficult to do with ceramic, though. I'm not a mechanical engineer.

Sorry I delayed my response so long; I'm unaccustomed to responding in these places and needed to get something set up to host the picture of my ring that shows what I'm talking about (though it's not as sharp as I wanted since it's using my phone).
My ring with inlay separating