Ok, thank you.
I will monitor the behaviour as from now.
Maybe I have some chanches making the arduino ethernet (as a client ) doing the request to update the new ip.
If someone is interested in this, too, there is an API Integrate with No-IP DDNS - API Information
Can the Ethernet be Client and Server on the same time?
Will I first have to stop the server then start the client then do the update, then stop the client and restart the server (?)