Try just a simple restart of the TC or restart of the network.. in order .. modem.. wait 2min.. TC.. wait 2min . then the client computer.. see if the TC reappears. if not you will need to do a hard or factory reset and start over. It is common enough on Mavericks to lose its marbles.. a good reboot will usually remind of it of where everything is.
Make sure ipv6 is set to link-local for whatever network client is being used.. that means setup in the computer.
And I do recommend using short names on the TC.. not apple names..
Keep names to <20characters.. <10 even better.
No spaces.. and pure alphanumeric.