Any specific reason why you're using APEv2?
I'm asking, because this is the root cause of the problem you're seeing. In Mp3tag, tag versions are prioritized in this order ID3v1 < ID3v2 < APEv2. So if the file has an APEv2 tag and you've enabled reading of APEv2, this tag gets displayed.
If you then write the tag, and have also writing of ID3v2 enabled, the tag that was displayed gets written to the ID3v2 tag.
Since the APEv2 tag of your test file doesn't contain
RATING MM, it isn't available if you read APEv2 and overwrites the ID3v2 tag on save (and eventually removes the
RATING MM from the ID3v2 tag).
So if you don't have a specific reason to use APEv2, I'd disable reading and writing of APEv2 (which is also the default on new installs).