The plugin does not automatically update tax rates in the sense of silently changing your shop settings in the background, because there are so many different VAT rules across Europe and elsewhere (about which goods go into which classification, e.g. standard rates and a large selection of different reduced rates) that this is not practical.
However, the plugin, in the “Readiness Tests” tab has a facility to automatically email you if any of the rates in your tax tables do not match any currently-known tax rates. VAT rates are not subject to change at arbitrary times, but only potentially on the first day of a quarter. As such, you can also manually check VAT rates on this date if you wish. Also, in the WooCommerce tax tables settings, there is a button to add/update all EU countries in the table at once (so that instead of adding or updating 27 rates, you can press a single button), using standard rates or the most common reduced rate for a county:
Posted in: WooCommerce European (EU/UK/Norway/Switzerland) VAT Compliance