I did run some tests in your website, i have added even more than 20 items to cart, once i open the shopping cart page, i saw all of them, i didnt notice any error or failure. By the way, the problem you have talked didn't make any sense to me, our template has nothing to do with adding products to cart, running the steps or any core functionality in Virtuemart. Our VM template is just stylizing the original virtuemart with some touches to make it look better.
Did you touch/edit the category browse page's "add to cart" button codes? Because i am seeing the "quantity" boxes in your website as there shouldn't be the quantity boxes in our VM Template's "category browse page".