Do you have any third party font manager software running?
Are the fonts installed under MacOS or are they in the particular document file's “Document fonts” subdirectory?
What format are the fonts? OpenType, TrueType, Type 1, .dfont?
There is a third party font manager installed, (Font Explorer X Pro), but I'm not using it. I just use Font Book.
I'm not sure where the fonts are. Often, I first open the file and InDesign does not ask for any missing fonts. They could be in the system fonts folder, or they could have been loaded for a previous job. Then, after closing the file and re-opening it it says fonts are missing.
I've never paid attention to what kind of fonts this happened with.
When you save, are you saving in the same folder?
Yes. Sometimes, I don't even save– Open file, looks ok, close file, reopen file a few minutes later, then fonts are missing.
If the Font Xplorer autoactivation plugin ins installed in InDesign, remove it and see if things change.