Mine was doing the same thing, but I think I just figured it out 2 days ago… When you turn on NHL 07, press the circle “Xbox” button to bring up the Live/User Account info screen. Log in as either a user or an Xbox live account. You may have to watch the annoying demo one more time, but from then on it will save all of the info there for ya.
Also if you DL the roster updates, I think you have to be logged into that account to actually be playing with the updated.
And post your gamertag so I can play you guys in some NHL…