I finally found a resolution to this issue. The 2.0 update moved the logic that displays the shipping methods on the cart and review order pages to it’s own file, with some changes. If you are using a modified template for these pages as I am, by removing the code that displays the shipping options and pulling the new file with the following code it should work properly. At least it did for me, good luck.
<?php woocommerce_get_template( 'cart/shipping-methods.php', array( 'available_methods' => $available_methods ) ); ?>
I am having this issue as well after updating to 2.0.3 on my staging site. However, changing the selection to a drop-down list did not fix the issue, it is still de-selecting after the price is updated.
It seems that the price is being updated properly, however when I try to complete an order i am receiving a validation error of ‘Invalid Shipping Method’.
Any insight would be much appreciated, Thanks,