This has all the signatures of a DDoS attack against iTunes Radio.
britishaussie's links show that iTunes has a list of categories of radio stations. Clicking on a category causes a request to an Apple database of radio stations in that category. Sometimes, the database requests work, usually they fail. Some categories fail much more cosistently than others.
The Apple response that they can't see any problem is because they used a computer inside the firewall that has sheltered access to the database.
By repeatedly trying, I have managed to get the lists of radio stations for all except the following categories:
Alternative Rock
Eclectic
Electronica
News/ Talk Radio
Top 40/ Pop
britishaussie's solution has the same problem as iTunes: when I try to use that method to get the list of iTunes radio stations for the above five categories, I always get an error. (For other categories, I sometimes get an error, and sometimes get the list of the radio stations, or I can just keep clicking in iTunes and eventually get the list.)
Apple must have some defences against DDoS as evidenced by the fact that, if one tries over and over and over again, one can obtain access to the iTunes radio stations in every other category, except those five, where the attack seems to have completely overwhelmed all of Apple's anti-DDoS measures.
The fact that no one has any idea of the appropriate corporate response to a DDoS attack is the most likely explanation of why Apple refuses to release any information about the problem.