"Disconnected from Xbox Live"

Whenever I go to play a XBOX 360 game I’m getting this message saying “Disconnected from XBOX Live” even tho my wifi is just fine. If I try signing back into Xbox Live I get an error message. What can I do about this?

The 360 would disconnect you if the game was not up to date. Also, if you are on Xbox One, make sure the game is backwards compatible. Beyond that, I am not sure. Good luck.

Is it possible to test it wired to check whether wifi is an issue?