I believe that AnyConnect sets a registry key that restricts the machine, to a single user login, so you can't be logged in with two users at the same time. The key can be change manually
http://www.cisco.com/c/en/us/td/docs/security/vpn_client/anyconnect/anyconnect31/administration/guide/anyconnectadmin31/ac04namconfig.html#pgfId-1221429