If you can’t sign into your Xbox Live account on Xbox 360, here are some steps you can take to be able to sign in again.
First, restart your internet modem and power cycle your Xbox 360 as well. Make sure your Xbox 360 can connect to the internet. When you perform a network test, you should see that your Xbox 360 console can connect to your network and the internet. The last step of being able to connect to Xbox Live is the issue if your internet is working fine.
One easy fix that has worked for a lot of people is to disconnect your wired internet connection and connect to a new Wifi network. Not only do you need to connect to a Wifi network, you need to connect to a different network than the one you have been connecting to. If you have a Wifi extender with a different network name, that would work.
You can also activate a hotspot from your phone and connect your Xbox 360 to the hotspot. For whatever reason, by connecting to a different internet network, you will be able to sign in to Xbox Live again. Connecting to your phone’s hotspot won’t work if you want to play online games, but at least you can update your profile and see it’s not a profile issue. Hopefully Microsoft will resolve the issue fairly quick. After a few days, you can try connecting to your ethernet or default Wifi network again.