Here are the steps to recreate the issue
1) Visit cheapasprints.com
2) Click on a product page (i.e business cards) - http://cheapasprints.com/shop/category/cheap-350gsm-business-cards/
3) Click on a single orange price box and add the item to the cart
4) Proceed to checkout / delivery details
5) You will see that a particular delivery option is selected. Click on the blue "create account" button which will output the relevant sections the customer has to complete
6) If the ship method is preselected to delivery, click on the collection radio box and you will notice that the delivery section in the checkout form has not disappeared. Similarly if the preselected radio box is collection, click on a delivery option and you will notice that the delivery section in the form does not appear. Customer has to select this twice for it to work.
I have also posted a video related to the issue which can be found here: http://screencast.com/t/UWKjcm0B