To resolve this, first try to refresh the notification page you have been presented with. If this works, you will be taken into WHM with no further problems.
If that does not work, you'll need to manually refresh the file yourself.
This can be done as follows:
1) SSH into your VPS as root using a tool such as PuTTY - available from http://www.chiark.greenend.org.uk/~sgtatham/putty/download.html
2) Enter the following commands and hit enter:
Above; the first command is used to shutdown the firewall we install by default. Sometimes, this can prevent connections to the cPanel server. If you are not using CSF, please stop any firewall you have installed. The second command initiates the cPanel license keychecker.
3) Attempt log into to WHM. If you still cannot log in, wait for about 60 seconds, then run the above command. This should sync the key and let you in.