Upgraded to OS X lion and now I cannot…: Apple Support Communities. According to JErnesti it appears that by uninstalling avast it solved the problem. That is a reasonable thing to try if you have installed Firewall/Anti-virus or anti-malware software like Little Snitch.
Apparently some users have had problems with Cisco AnyConnect Software and 10.6.8. It seems that after installing the newest OS, that CAC has problems getting and staying connected. This software has had problems for some people for several years, and here are some solutions to fix them that have worked for others.
Upgrade your version of Bonjour or disable it. This can be a problem for machines that are 10.6.3 or earlier.
Use Ligion to restart the Cisco VPN service. Google this term and you will come up with the command used for this.
Uninstall and reinstall the software. This seems to fix it for some people.
Disable third-party software like Anti-virus software, firewalls or programs like Little Snitch.
Disable or better yet, uninstall old versions of Cisco VPN software.