I use this function all the time and it works well here.
The first thing I would check is the DAW plug-in preferences.
Make sure the "allow drag and drop" checkbox didn't get unchecked somehow.
Then I would try again, and after the dropbox turns green try dragging right to the desktop rather than a Logic window.
Doing this should put a file on the desktop that you can double-click and make sure it's a valid audio or MIDI file.
This will tell you if the problem is with Logic, or if the files you are generating from BIAB have a problem.
Hopefully this helps.
Edit: Wow I'm a slow typist !

Yeah, what Peter said above me.
- Jay