I have the same issue. My automatic downloads for music only is on on both my iPad and iPhone with the latest software with the same Apple ID. If I purchase a song on my Apple TV iTunes Radio it does not download to my other devices or even Mac. If I go to iTunes on my Mac and check for available downloads there is nothing to download.
I have to manually go to the song and download the songs from the cloud and it does not move it to my Purchased playlist.
Same issue for me. Does not show up on computer when I "Check for Available Downloads." I had to search for the song in the store and try to purchase it again - then it says "You have already purchased this song" and gives me a button to download it to that device.
This is really pretty screwy - I want Apple Radio for that very reason - so I could purchase a song in the Tunes Store as I listened. At this rate, I may go back to Pandora.
OK, I seem to have solved this after working through a few related support articles. Here's what I did:
1. I searched for the missing song track using the instructions in Apple support article (TS1408) via the Finder and could not find it, either in my properly located (and full) iTunes Media folder, or anywhere else on my hard drive (I did a global search as well).
2. I then proceeded to a second article about re-downloading purchased content (HT2519). At Step 4 (in the section for iTunes 11 or later) it says to be sure you have "Show iTunes in the Cloud purchases" selected in the iTunes>Store Preferences pane. I checked there and I did not have it selected on either of my two computers (for good reason since I have never done any such Cloud purchases before). Anyway, as soon as I selected that and closed the Preferences pane my iTunes library window updated itself automatically and there was the song in question with an iCloud symbol beside it. I clicked on the song and it began to play, presumably from the Cloud. I then clicked the cloud symbol next to the track and iTunes quickly downloaded the song into my library on my desktop iMac. I took the same steps on my second Mac computer with the same successful results. There was no additional charge for the downloads, as I had already bought it via my Apple TV.
I have not attempted to duplicate this yet since I have had no need to buy another song via iTUnes Radio on my Apple TV. But it did fix the problem I had at the start of this thread. Appreciate any feedback from others if they try this.