Label this as unconfirmed for the moment (we've since written Microsoft for comment), but one tipster told us about a refurbished Xbox 360 that couldn't connect to Live. When he called Microsoft, they said that his box had been "banned" from the service. We attached the email after the jump.
...[a friend]called me up when he ran into trouble getting [his refurbished Xbox 360]to work. So I came over and started trying to get the media extender and Xbox Live working. While we had no trouble connecting to his network and getting the media extender working, the Xbox live connection kept failing, with an obscure error code (the whole X = 0000 0F01, W = 0000 0201, kind of cryptic message).
So I called Xbox 360 support, read the error message to them, and discovered that there was a lifetime ban on the box, it could never be connected to Xbox Live (and thus was useless to my friend).
I explained to the representative that this was a Microsoft-certified refurb, and that my friend had just purchased it. She said that it didn't matter, Xbox reserved the right to revoke Xbox Live privileges "with no recourse," and that was done by identifying offending consoles and banning them.
While we've heard colloquial accounts of modded boxes getting banned, we've never heard of problems with refurbished models. If the story is true, it essentially nullifies the Xbox 360 resale market. The risk is too great for consumers to purchase Xbox 360s that may not work on Live. We'll give you an update when we hear something back on this rumor.