My iTunes Radio will shut off every few hours and ask me if I want to resume. Is there a time limit on how long you can stream iTunes Radio and if so can it be disabled?
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.
I think this is a standard practice of streaming services because they do have to pay (a tiny amount) for each track they play, so they want to make sure you are still there and aren't streaming their money into an empty room.