WooCommerce has two very nice debug features often overlooked. One of them being the Shipping Debug Mode. This tool will disable shipping rate caching and should always be tried out as a first step, when dealing with WooCommerce issues related to shipping.
Go to WooCommerce -> System Status and navigate to the Tools tab. The relative URL is:
Scroll down to “Shipping Debug Mode”, tick the box and hit Save changes.
Here is a small screencast in addition.
View this screencast in a new Tab.
Beware that this will be active for all users. Deactivate it again after you are done.