You're sure you have write access on the external drive? That is the only reason I can think of if the tags for the MP3's are not written to the media. It might also look like you can't update the library for the next restart.
I would try this.
1. Make a backup with some tag changes. Number plays or something else that makes you sure if things are saved or not.
2. Restart MC
3. Check the tags. It they are not stored, try to restore the library backup.
If the restore does not help, you probably have some problems writing to the location of the backup file. And possibly for the location of the default library.
If this is the case, I would try to uninstall and reinstall MC to another directory that you KNOW you have full read and write access to. Keep away from Program Files. It's a bit limited. After you have installed MC again, you can restore the library backup and try the same things again.