I went through a lot of before figured this one out. Many of the forums that I went through had solutions where registry settings needed to be changed, and internet connection sharing needed to be turned off. None of that worked for me.
I finally figured out that I was using client version 3.0. This version allowed me to initially connect to the vpn server, but after the connection handshake something always went wrong. The 3.0 anyconnect client was given to me by my customer, but their server was really only compatable with a 3.1 version if it was running on a new version of Windows 7. Complicated huh?
Cisco won’t allow you to download a 3.1 client unless you’re a customer, but there are many places on Google that have it. Anyway, once I upgraded to 3.1, the problem went away.