are you behind a router? If so, using a static IP would be trivial. "man ifconfig" will be very enlightening, Debian probably has some wizard to make it even easier.
If you have your xbox going straight to the internet..well first of all thats a really, really really bad diea. second of all, if your ISP is using DHCP, then you either need to have a client, or set your IP statically to an IP you know is good...using one you've managed to grab previously is the best place to start there.
I have friends runnign linux on the xbox, and they don't seem to have had the issues you're having. something else bad has clearly happened, i suggest getting on some "xebian" forums and finding out