I have had this problem too, except that I have had this problem for stations that I have definitely listened to before in the Model S. I never used TuneIn before I got the Model S.
Now some of the stations refuse to play. Sometimes, if I select one of these "dead" stations, I won't be able to play any other stations unless I switch to a different media source and then back to TuneIn. Resetting the screen doesn't seem to help. Now, I have noticed that two of these stations won't play on my mobile phone either. However, one of the stations that won't play in the Model S still plays on fine on my phone. What is worrying me is that more and more stations seem to be going dead.
I thought maybe removing them from my favorites list and then re-adding them might help, but then I ran into a different problem. The Soundtracks category, which used to either be a top level category or maybe it was under Specialty, is now missing! When did that happen? Now I can't find my video game stations, even the ones that are still saved to my favorites and still working.
Even though your TuneIn account info is stored in the Model S settings, it doesn't seem to be of any use. I tried signing in and out. On other devices, such as the mobile app and website, your favorites are pulled down from the cloud by logging in with your account. The Model S app apparently only cares about what has been set locally.
BTW, my issues are with live streaming stations not TuneIn "shows" (podcasts).