This has been happening to me since December. I've read a lot of similar posts here and none seem to be getting resolved. I'm at work so I don't have all the details from the "START HERE!" post, though I plan on adding them when I get home.
What happens for me is that I'll power up the 360 and my Live account logs on automatically. Then whether or not I start playing a game, I'll get disconnected from Xbox Live. This could happen within a few minutes, or up to an hour after. If I test my network connection it always tests as working fine and Xbox Live is up and fine and I'm able to reconnect. This happens both with wired and wireless connections and happens when I connect to my neighbors wireless as well. I've disconnected everything from the wall to the xbox, tried connecting with and without the routers, and made the system pull down all updates again and it's still constantly disconnecting me as I play.
This is the exact same equipment I've been using for years and have never had an issue till December.