Hi Jack,
Sorry for the delayed response, I checked your site yesterday but it was having some PHP problems; took another look now and have a fix for you. Because your site is using AJAX to swap between pages, you need to tell the timeline widget to initialize again after navigation happens. By default the Twitter widget is only initialized on initial page loads. You can trigger widget reloads by using the JavaScript twttr.widgets.load() after your page navigation script has completed.
Hope that helps,
Ben