Howdy Alex,
I would love to help you with this. Thanks for sharing the link.
I like your theme. I believe it is actually the culprit though. Your theme appears to have moved the month title outside of the ajax area. This means that when you click next/prev, it simply can’t update that area because it’s outside of the updatable region. Really the only straightforward solution is to move the Month name back into the ajax region. Did you design the theme? If so, can you move the title back into the div#tribe-events-content? If you didn’t design the theme, you should contact the author and point out hte bug to them. From there they can release an updated version that fixes it.
Does that all make sense? Will that work for you? Please let me know.
Cheers!
– Brook