Is there a time limit on how long you can stream iTunes Radio?
You should count on it shutting off pretty much at the two hour point:


  Why does the music stop playing after two hours?
  
  iTunes Radio will time out if you don't interact with your system or
  device for approximately two hours. If this happens, simply access
  iTunes Radio again and choose a station to continue playing.


From: http://support.apple.com/kb/TS5181 - Common questions about iTunes Radio

If you set a timer and change the channel about 20 minutes before things are about to stop, my experience is your 2 hours starts anew. I don't know if there's a practical limit on how long you could keep this up or if some pause is eventually enforced on the server side.