I've spent about 3 hours total with xbox support and I'm not having any luck. Typically it works for the duration I'm with them on chat, then when I get off about 5-15 minutes later it disconnects.
When I test my connection, the network and internet connect, but the xbox live will not. Sometimes it reconnects randomly for up to an hour before disconnecting again. I've done traceroutes during disconnects to my internet provider and everything is stable. I called my internet provider and he said that they are having "a lot of xbox LIVE" problems. He said it would be fixed by connecting my ethernet cord straight into the modem. He then told me that it was xbox's fault and I had to wait for an update. The modem connection worked for a while, but then within an hour was back to disconnecting.
I have rebooted my router, modem, deleted corrupt files, cleared system cache, entered port numbers for 360, opened my NAT settings, checked for data corruption in my profile, tried using my wireless adapter, deleted the last LIVE update and redownloaded it. Again it appears "fixed" but within an hour it loses the connection again.
I have not had problems disconnecting for the last year and half in my apartment. It just started on Presidents Day when I got back from a trip. (I had taken my xbox with me and it worked fine at the other place on LIVE).