i bought my xbox a few weeks ago and this has been happening since i've got it.
i can go into multiplayer but a couple minutes into the game it gets really laggy, i lose connection, and thendisconnect from xbox live.
i also get disconnected from xbox live if i leave my xbox idle for 10mins or so.
i do not have any other things up on my laptop like youtube or twitch which would slow down my connection.
if it helps, i can play custom games online with my friends and not get disconnected, just when i play normal online multiplayer it happens