Woocommerce checkout not saving shipping choice from cart page

Hi,

Our customers are having issues for the following:

They choose their shipping option in cart, but when they go to the checkout page, woocommerce defaults their choice to the first shipping option. This has caused several order issues.

How do we make sure the shipping choice stays the same from cart to checkout page?

Thank you.

The page I need help with: [log in to see the link]