File this one under Works as Designed, although your question is a little unclear. Using stateful information within a cached block or the template of a cached block will lead to one state being added to the cache, and your conditional won't run again until the cache expires the entry.
As for a solution, it's not 100% clear from your question how you've set this up. You say you have a
mini-header.phtml
mini-footer.phtml
Then you have some conditional logic, but you don't mention where this conditional logic is.
Then you say you have a CMS static block called Footer Links.
You don't mention how mini-header.phtml or mini-footer.phtml are added to your layout.
You don't mention how you're adding the CMS static block.
All these details will matter if you want to find a solution to your question.