So I'm having the weirdest problem with Live for the last week or so...
It can't connect to Live initially. When I boot up my 360, it says 'Can not connect to Live.' Trying to do so manually also gives me the same error. However, going to "Test Connection" leads to it connecting fine. I don't mean actually testing my connection, but just selecting the option. It goes to the "Wired or Wireless" options, connects to Live and everything works fine.
It's fairly annoying because it's a lot of extra steps just to connect, and it's only been happening for a week or so.
Okay, so I cleared my cache and it allows me to connect via dashboard... but as soon as I launch a game it disconnects me from Live and won't connect while in game. If I choose the option to test connection, as soon as it leaves the game it connects again.