The Youtube logo stopped appearing in my Apple TV several weeks ago. What can I do to retrieve it?

Sorry but your issue has nothing to do with Apple networking. I would suggest that you re-post to the AppleTV section of these Apple Support Communities so that experts there could offer you a potential solution.

What generation of Apple Tv do you have?

Identifying Apple TV models - Apple Support

If you have a first or second generation Apple Tv, then Youtube is no longer supported on those models, as Google removed support for older Youtube apps.

It affected other devices such as Smart Tvs, and Blue Ray players that also had the older YouTube apps.

Certain older YouTube apps will no longer be supported after April 2015

https://support.google.com/youtube/answer/6098135?hl=en