I have a 2 year old Xbox 360 S. My Xbox will not stay connected to Live when trying to play games online - but it stays connected when on Netflix.
Each time I sign in it makes me go through all the steps of setting up my connection again on the dashboard. It always connects to the internet but sometimes it fails when attempting to connect to Xbox Live. Once it does connect and I load my gamertag and sign in online, as soon as I load a game it signs me out again and I have to resign in.
It does not let me join the majority of matchmaking games and it just sits there loading. In Halo 4 it disconnects before the game starts or breifly after (~30 seconds) and says "It appears you do not have a connection to Xbox Live". However, I can still see my friends list, etc., but nothing loads when you attempt to access it. Then after a few minutes it disconnects me from Xbox Live and I have to start the same process all over.
It does this when I connect wirelessly and with an ethernet cord. It is not our internet as we have 3 Xboxes between myself and my roommates, and mine is in the room with the router. The other 2 Xboxes connect fine.
I have tried emptying my harddrive cache and I always download my games to my harddrive.