This one troubled me for a little while, now I finally managed to reproduce it in a small file, so you can analyze it.
A song was converted from mp3 to m4a using dbpoweramp (with nero encoder).
If I open it with WinAmp, Floola or iTunes, the genre tag is correctly detected as "Anime".
But if I open it with mp3tag and click the "save" icon (without actually changing any field), then the resulting modified file shows an empty genre tag when opened by the above software (but still retains "Anime" if opened with mp3tag).
It seems that the genre tag is changed in a way that mp3tag can still read it as "Anime" but others cannot.
The sample m4a is located here:
http://www.davideorlandi.it/storage/mp3tag/vitaminc.m4a
The copy changed by mp3tag is here:
http://www.davideorlandi.it/storage/mp3tag/vitaminc-copy.m4a
Mp3tag version used is 2.42b (tested with 2.42 too).
Interesting note I: sometimes (I should say "often"), files encoded to m4a/aac using dbpoweramp show the same behavior even without being touched by mp3tag.
So I suppose this might be a problem with ambiguous standard definition for the mpeg4 tags, and not with mp3tag. It would be good to have a workaround in mp3tag, though. 
Interesting note II: if I change the genre to a custom one (for example "xyz") and save, the genre IS read correctly in winamp and iTunes. Apparently the problem only happens with standard tags.
Thank you for your patience.