Yes, you will loose root access after every update. If you don't wipe Data in TWRP you won't loose your apps but it is recommended if comming from Miui stable rom.
Xiaomi.eu ROMs are based on China dev - so they should have built-in root, too. But they haven't. So, something is wrong about what you say...
But yes, updating always removes root - something that is easily understood when you know that the new ROM just simply overwrites the old one. Consequently, everything you did in the old ROM is lost, not only root.
