Nav menu not updating when I open page with different nav menu

I am working on a website

I think the custom theme my client is using is not loading the header every time you load a page, only the first time you load the website. While this looks nice, it doesn't work because I have a membership area with a separate menu (this was not in the original theme, I edited the theme to make it work). The membership area is closed off though so you cannot see it. I can give a WPMUdev staff member the login details though, if you would just PM or email me.

To recap: when a new page is loaded with a different header, the new header is not shown. Only the old header remains.
My question: How do I fix it/what do I edit to fix it?