Music Library gone

unless you have the old big alu appletv then your music lib is not on the appletv it's accessed from a computers shared itunes lib the computer needs to be turned on and running itunes

and it being across the network there are some ports which needs to be allowed by the router and firewall of the computer

TCP and UDP ports used by Apple software products - Apple Support

If you are referring to purchased items through the music app, try signing out of and back into your iTunes account.