Nowadays there's no clear cut way for modders to stay on live. However, I have done what appleguru said a while ago, and i'm still on live ... 3 months and still going strong.
The best thing to follow now in my opinion is the marriage theory... where the hard drive that you used to sign in for the first time, must stay the same, or a ban.
Playing on live with a modded xbox is basically playing russian roulette..... Some get away with it (like me), and some get shot in their ass (like deathbringer).
Even when u follow the mariage thery, don;t forget to only log on live with the default bios. Turn off auto sign in, and if you can, put ur account on a memory card.
Unplugging the network cable when using the hacked bios won;t hurt either.
Hope this helps.... and good luck