You could probably try changing the update cart behavior on the page to use Any form post instead of using the update button click trigger.
Another solution may be to add a hidden form element to the form. I think IE doesn't push the button automatically unless there is more than one form field on the page. This has been a problem in IE for ages and I think adding a hidden field will fix it. That is why it works with more than one item in the cart, since that means there is more than one input field. You may have to use type="text" style="display:none" instead of inputy type="hidden" but one or the other should get around the problem.