If you take a look at the product page it's not just a scale. [0] It's a 'smart body analyser'. There are several features that probably wouldn't work if they turned off the servers. For example if gives you the weather forecast when you weight yourself. Wifi sync and the companion app are also billed as main features. I would guess shutting down the servers would be fine providing all of this stuff still works and the device can maintain your history as it is supposed to show you trends. So it may still function as a scale but it's not being sold as a scale - it's not even called a 'scale'.
[0] http://www.withings.com/uk/en/products/smart-body-analyzer
Edit: Also under EU law if a product does not function as advertised you have a minimum two-year guarantee. So the company "must repair or replace them free of charge or give you a price reduction or a full refund." Unless the product continued doing everything it says on that sales page I linked Nokia would probably have to refund me and in many countries in the EU you are given even longer that the minimum required two years.