Due to this problem, I actually migrated my site from Nginx to Apache.
But that didn’t solve the problem.
I suspect it could be something I did while the site was hosted on my Nginx server: I did some CHMOD and CHOWN stuff. However, this still does not explain why everything worked fine in IE and Chrome, but not FF.
Are you using WooCommerce 2.0.14 + WP 3.6?
Did you untick “Clear cart when logging out”?
Did you also use a pretty permalink?
Thanks!