Some games automatically try to connect to Xbox Live whether you want them to or not.
I got banned because I started to play a game on my HDD and it automatically connected to Live. I saw what it was doing but couldn't get to the Xbox fast enough to turn it off and prevent the connection. I was banned immeadiately.
I read all the forums that I could find on modding, and using Live with a modded Xbox, before I modded mine and never saw a post saying that it would be best to disconnect your Xbox from the internet BEFORE playing a game on your HDD.
My recommendation is that you disconnect the internet feed from your xbox before EVER playing a game on your HDD to make sure that it is impossible for your modded Xbox to connect to Live without your express desire for it to connect. If I would have just done that, I could still play on Live if I wanted to.
On another note. I phoned the (800) 4my-xbox number and after a long discussion they told me that my Xbox SERIAL number was banned permanately and that my Xbox would never be allowed on their service again. (Anybody want to buy my Live Starter Kit w/Crimson Skies HRTR?)
I hope that this will help some people out.