the Vista WGA program does not like hardware changes, as you've noticed. it's also triggered with driver updates, even microsoft certified drivers or drivers via windows updates, no exceptions.
you typically have a 3 day window to reactivate over the net or via a phone number, but in rare situations, you might be stuck in an activation cycle without the ability to re-activate, i.e. if you haven't activated properly before, or there's something on the system preventing you from altering the registry, i.e. a firewall or antivirus service. or a damaged registry entry for the activation service, etc. etc.
there's very little one can do to avoid microsoft activation errors other than try to re-activate windows manually to reset the internal hardware database, then update CIS again. if you ring up for advice, they won't be able to tell you directly how to reset that internal DB, but until it's reset, you'll always be on the cusp of re-activating when hardware/drivers change. there are other alternative methods of activation, but they always rely on the service being able to reset certain registry flags.
three possible fixes : install the video or system drivers or another set of updated drivers to hit that wall again, then reactivate over the phone, reboot, and once you've got around microsoft's licensing harassment, update CIS.
manually re-seat and re-activate, the instructions are on the microsoft website and others. i.e.
http://support.microsoft.com/kb/950755/en-usor, update CIS again, reboot and see if it triggers reactivation again.