I'm not really sure wich is your problem. If you use knoppix network default configuration, it will ask for an IP every time that starts, so, depending your LAN configuration or your ISP you will get a diferent IP every time.

What for you need an static IP? You will ned an static IP if you are serving web pages or have a public FTP. And, in this case there are workarounds.

If you can specify why you need an static IP maybe we will be able to find a solution.