Why does the cart not carry over it's values?

The shopping cart on our store is behaving oddly. If you go to http://store.currentmm.com/audreyassad/store/products/fortunate-fall-vinyl/ and select “add to cart,” the shopping cart widget seems to update. However, when you go to checkout, the cart shows as empty and refreshing does nothing.

I can reproduce the issue in Firefox and Chrome. Currently, our site has enabled only the MarketPress plugin and the WPMUDEV update plugin. I switched our basic “FlexMarket” theme (from MarketPressThemes.com) to WP 2013 and got the same result.

Searching the forums, I found at least one person with the same problem, but the solution for them did not seem to have anything to do with our setup. Thoughts?