Marketpress not removing/updating


I've just updated to the latest version of Marketpress (I'd been a bit terrible and not updated for 2.5 years...), and I'm experiencing a problem with the cart.

When I try to delete an item from the cart, and then return to the cart, the item is still there. And then when I try to add a new item, it doesn't appear. However, this doesn't happen when I'm logged in as admin. And the items do show up eventually when I move through the checkout pages and reach 'review order'.

Not really sure what's happening and why, and couldn't find a solution in the forums, so would appreciate some help!