Just from browsing your website, from the way it is behaving. it is a caching problem.
This does not happen when the server is correctly configured.
Ive used woocommerce from early versions, continuously updating and i am now on the latest release via github.. this has not been a problem and my site is fully functional..
see for yourself here.
EDIT: i also suppose this could possibly be the way your server is dealing with the ajax requests with a caching issue combined? switch to twenty twelve or something without ajax features :).