I have exactly the same problem with anyconnect 3.1.02040 and windows 8.

1st connecion to my VPN is working well. Teh the disconnexion is taking a very long time. Then, any way to use Internet of to start a new connexion (it seems that Anyconnect removed the IP configuration and DNS) and did not update it back after disconnecting: the only solution is to rebbot by switiching off the computer because a normal reboot takes seems to be infinite.

I would also support for any resolution.