I've been noticing this issue on and off for awhile now, but just recently decided to try to figure it out, so I'm not 100% sure how to reproduce the circumstances. It seems that only sporadically, I will make a change to the album artist in MP3tag, that doesn't carry over when I import files into Mediamonkey. I usually just change the field via Mediamonkey. The files I noticed this issue with today were flacs, but I think I've seen the issue with mp3s as well.
Could you check the extended tags whether you write "ALBUMARTIST" or "ALBUM ARTIST" and whether you have a mapping for one of these field names?
So I'm not super familiar with this beyond a little bit of research today, but I think 99% of my edits are applied to the "ALBUMARTIST" field, and that is the field that Mediamonkey treats as album artist for sorting purposes, but I think for some reason, some of the edits that I do in mp3tag are being applied to the "ALBUM ARTIST" field.
I'm noticing that the flac files I was having an issue with today have 3 fields in extended tags: "ARTIST" "ALBUMARTIST" and "ALBUM ARTIST", whereas many other files only have "ARTIST" and "ALBUMARTIST". My theory right now is that mp3tag is applying changes to "ALBUM ARTIST" for these few specific files, while for others it applies to "ALBUMARTIST". I don't have any mappings as far as I can tell in settings that would be affecting this.
Did you check Tools>Options>Tags>Mapping?
Honestly, MP3tag does not have a mind of its own so that it sometimes writes ALBUMARTIST and sometimes "ALBUM ARTIST".
Did you check the extended tags dialogue and see which fieldname you find in the files where the data does not "stick"?
I'm actually starting to think my issue might be with the way Mediamonkey treats flac files. Looking at the extended tags and making some test edits, it appears mp3tag is functioning as it should. Thanks for taking the time to comment, it gave the issue some clarity for me.