Very strange issue with permalinks

Hi there – I have a really strange problem with our site, and I think it’s theme related but was hoping you might be able to help.

I’ve recently migrated the site to a new hosting provider, and the site is running fine, however, whenever I try and save an old post the permalink structure changes to something completely different. It changes to another permalink for another page/post.

You can see it happening here: http://screencast.com/t/iJp9G4xU

Any ideas what the problem might be? It’s happening on every new post. Also, the Visual Composer doesn’t load as default, which it used to.