The problem is that a hardcoded "Media" is used as virtual folder in ezwebdavcontentserver.php. When retrieving the list of folders in the Media tree, paths to the folders are constructed like this:

in 3.9
the current script URL + the name of a folder

from 3.10 on:
site access + virtual folder (if not Media tree) + the full url alias of the folder

when the urlalias_compat transformation group is used to make url aliases though, the start of the url alias of a folder in the media tree will not be "Media" but "media".

from webdav.log:

2008-07-18 19:42:53 : Check virtual folder: site 'ccb' in 'media/audio_resources'  [CS:getVirtualFolderCollection]
2008-07-18 19:42:53 : Unknown virtual folder: 'media' in site 'ccb' [CS:getVirtualFolderCollection]

Maybe a solution:
use the real url alias of the media root node to check and build paths with