does it show up when the TV is on?
is your network "strange" (more than one router, or other devices upstream of you)
there is no home kit setting on the aTV, as long as you're plugged into power, connected to the internet (via wired or wireless) and logged into your appleID, it should be working.
try rebooting your router and the aTV,
it would be pretty silly for apple to make a device that allows you to access your home when you're not there, and to have that device automatically shut itself down when you're not home.