Thanks for your question and I am sorry to hear about that connection issue. After conferring with some of my other techs we haven't encountered previous issues or complaints about connecting to Xbox live on a PC. This leads me to believe that something unique may be happening on your machine.
Without knowing the specifics I don't want to venture too far into conjecture but my initial thought would be that our filter is interacting with either your network or the Xbox live app itself in an unconventional way. If you utilize the custom blocklist it is also possible that a specific URL necessary for Xbox live to function properly is on your block list.
I would honestly recommend calling in to our Member Care Department so they can take an in depth look at both your machine and your block list. You can also test this yourself by temporarily disabling your filter on an account level, refreshing Covenant Eyes on your device, and then trying to connect to Xbox live. If you are a restricted user you will need to have your Administrator do this for you.
Our Member Care Department can be reached at 989-720-8000.
Thank you and have a great day.