Items in shopping cart still there after checking "remove"

Items in shopping cart still there after remove.

Steps to reproduce:

1. Add to cart a product

2. Go to shopping cart

3. Remove product and update cart

4. Click on shopping cart again. Item still there.

See http://samplemosque.ialif.com/store/

Note that this appears to be a new problem as I was solving the problem reported here. https://premium.wpmudev.org/forums/topic/i-cant-checkout-with-marketpress

I was able to reproduce this with a default template and no other plugins activated but marketpress.