Welcome to justanswer.com, my name is ***** ***** I will do my best to assist you.
Sometimes all we need to do is turn the xbox off, then back on. And that resolves the live connection issue.
if that doesnt work, lets try resetting your network settings.. heres how.
After you have reset your network settings to factory defaults turn the xbox off, then back on. And then reconnect to your network. remember if its a wireless network you will have to select it and enter the password.
if that doesnt solve the issue, then let me know if its giving any error code when you try to connect to xbox live after we complete the above steps.
I strive to provide great service, and greatly appreciate a rating of excellent ( 5 stars ) selected and submitted below this answer or at the top right of the screen. I always answer follow up questions.Dustin S.Senior Technician and Network Switching Systems Operator / Maintainer.