I just spent a little time trying to figure out how long this thing was on McCoy's shelf. Dukhat's screenshots with Kirk are from 2x05 Amok Time, which might be the first time we see this part of the sickbay complex? I poked around in a few Season 1 episodes and didn't spot anything, and this would be consistent with the facts that the last Stage 9 set plan we have for Season 1 (09 Balance of Terror) shows that area still undeveloped, and we know there was a major overhaul here for the start of Season 2. I also checked 2x01 through 2x04 and didn't see any examples of the shelf. So for now I'm assuming that 2x05 was the saucer's first appearance.
The next chronological shelf shot I could find was in 2x08 The Changeling
(right), and the saucer was still there (judging by the shadow cast on the back wall).
Then for 2x10 Mirror, Mirror, they completely redressed those shelves for the
I.S.S. Enterprise and the saucer was not visible. In the very next episode filmed, 2x11 The Deadly Years, the shelves were restored but it appears that the saucer did not return. (Probably somebody gave it a moment of critical thought during the re-redress and said, "nahh.") I suspect it never came back; at least I haven't yet been able to find another instance of it. There's another visible example of it still being gone in 3x08 For the World Is Hollow, but I really only spot-checked a handful of episodes that I thought might have scenes in this area.
So considering that this was only seen in two episodes (barely in one, and almost not at all in the other), I have to say well spotted, Dukhat!
Where are those great close-up shots from ... one of the fan productions, maybe?