Hey ffejmi,
It sounds like you might have been in the same boat as me. I had iTunes Radio working fine for several days on my 3 year old MBP running OS 10.8.4, then it seems like it was perhaps on launch date of iOS 7 that I lost it. Just like you, I was listening to it, it suddenly stopped working and the button disappeared after a few minutes of clicking around trying to get it back on.
I followed through this whole thread trying to turn on "Internet Radio" in Preferences and clicking the "iTunes Radio" link in the store to no avail. Then I remembered I was running iTunes 11.1 beta.
So I tried just downloading the installer for the latest version from Apple.com (http://www.apple.com/itunes/download/), ran the install and voilá, iTunes Radio is back on and running.
Hope this works for those that are running the latest OS that are having the issue.