MC does not show a link info in the Image File field if MC actually uses an embedded image file. The field shows "Inside File" in that case.
After the "Inside File" text is visible it stays unless you make MC to update the library from tags and possibly change the cover art state if a suitable cover art file is found. (I suppose also the import system may update file data. I don't do global imports anymore so I have never experienced this.)
If the Image File field shows a filename (and possibly a path) then an embedded image is not used.
My MC has never lost cover art links (about 35000 at the moment) or the few embedded cover art images (about 150) I have, except once when the library got really screwed up because of a crash.
I checked an external tag editor and while MC shows the the cover art in the library the Mp3tag editor does not. Where is the cover art?
MC may support embedded images in some formats that Mp3tag does not. Some programs may also delete embedded images if they don't understand the format. What is the file & tag format?
MC does not actively monitor disk file changes. The way to check if the "Inside File" image is really present in the file is the Action Window > File Properties > Image display. If it shows only text then MC cannot find the image.