Hi Guys,
i too just fixed the problem on a custom theme by editing the file themename->woocommerce->cart->review-order.php
On or near line 83 the options or radio buttons for the dropdown list of shipping methods had this code which check the session if a option has been selected
selected( $method->id, $_SESSION['_chosen_shipping_method'], false )
i then replaced it with this
selected( $method->id, $woocommerce->session->chosen_shipping_method, false )
This fixed the problem.
Hope this helps.