I'm not sure that using GSSAPI is really a necessity. The most likely explanation of this issue is thatthe SFTP site used to accept private-key-based authentication until recently, but changed their policy to require a password authentication in addition to private-key authentication. This additional authentication can be done either by "password" or "gssapi-with-mic" authentication methods. I that case, I would expect them to inform you about this and make it possible to set the password. The you could simply change your code to:
_connection.Login(userName, password, key)
With GSSAPI, it is also possible to perform a password-less authentication, but for this to work, some kind of trust would have to be established between your Windows domain and their SFTP server's domain, otherwise password would be needed as well. If you don't know what GSSAPI is, it's far more likely that GSSAPI is just one of the authentication algorithms the server supports, not that you must use it.
Asking the SFTP server administrator looks like the best thing to do.
Rebex SFTP doesn't currently support a combined private-key/GSSAPI authetication, but if it turns out this is required in this case, we are ready to add it to the next release.
Are you able to connect to this server using any third-part SFTP client?