We might need to know more information to help, but here are a few options to look into:
1) As mentioned before, possible bad router, they do simply stop proper function sometimes.
It sounds like this isn't your problem if the other people that were on weren't kicked off either.
2) If someone else signs in on your account you will get kicked off, you could have someone "trolling" you just to annoy you. A message similar to "You account has signed on another console"
3) Sometimes you can have a "sticky button" on your controller, so if your sitting on the xbox menu and the "x" button sticks it will sign you out. (Stranger things have happened!)
4) If the console actually signs you out completely, this might not apply, but if it simply boots you out of a match or a game it is most probably your internet. This could be your NAT settings or it could be your IP. (I often get kicked out due to my wife
5) Depending on what you are doing when you get kicked off, if you are playing with friends who have DLC that you do not have, when the game tries to access the DLC for them it could recognize that you do not have it and that you are not able to access the
These are just the ideas that come to mind without more information, maybe it will help!
Did this solve your problem?
Sorry this didn't help.
Great! Thanks for marking this as the answer.
How satisfied are you with this reply?
Thanks for your feedback, it helps us improve the site.