You might want to give more information as to what behavior you're experiencing. I can sometimes get the page to "rerender" -- but it actually rerenders the entire page, not just MathJax.
In any case, MathJax only automatically renders content on the first pass and never re-renders content. In other words, something in the page's code triggers the rerendering.
From a quick look through your code, it seems like MathJax is never asked to rerender (just to typeset new code), so the problem might not be related to MathJax at all.
Hope this helps get you started.
Peter.