BT Hub? A wireless router? It could possible be a DHCP issue. Is your Xbox set to "automatic" are there other devices on your network? Do other devices on your network drop off randomly?
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Check your router settings and see if they are compatible with Xbox 360 and Xbox Live. Some router Security isn't capable of handing the Traffic that Xbox Live Produces.
Here is the Compatible Hardware List
If you go to http://xbox.com and click on
Sign In at upper right then go to
the Request A Call button will get you in touch with Networking agents who are familiar with this problem.