The links that lead to the sites to vote for Combine do not disappear after you click on them. I gain the CP bonus but the links remain active. The active links don't give out CP though if it hasn't been 24 hours.
Unfortunately, as this does not seem to be reproduceable and I have seen no other reports of it so far, we may not be able to offer any solutions. If this problem persists you should post it in the bug base for one of the developers to take a look at when they have a moment.