I have an Dell laptop running Microsoft Windows XP, a wireless card (Intel Wireless WiFi Link 4965AGN), and the CISCO VPN Client software (version 5.0.01.0600). The wireless connection worked fine connecting to the Internet, and the VPN client software worked when using a wired connection.
Unfortunately, whenever I tried to run the CISCO VPN software, the wireless connection would fail.
It turns out the problem was Windows' power management of the wireless interface. To fix this, get to the Windows device manager (Right-click on "My computer", select "Hardware" tab, and press the "Device Manager" button). Right-click on the Wireless Wifi Link, choose Properties, and then choose the "power management" tab. Turn off "allow the computer to turn off this device to save power". After that, it worked!!
My guess is that when the VPN is turned on, Windows incorrectly thought that I'm switching my Internet connection from the wireless card to the VPN; it then concluded that I didn't need the wireless and switched it off. I googled on this problem and didn't find anything, so I've put this page up so others can learn how to solve it.
I didn't figure this one out; Reggie Hines figured this out (without help from the vendor!). Thanks, Reggie!