I have exactly the same problem. WebDav with gmx media center crashes the app reliably when downloading a file. I can also confirm that the upload works just fine.
I cannot give you my gmx credentials (private email account) however, you can create an account of your own free of charge. WebDAV functionality is included in the free version.
Would be really great to see this working, since I currently don't have access to another WebDAV server.