Not sure whether this is technically a different solution...
My 12yo daughter tried to download an album directly onto her iTouch 3. All of the songs but one worked. Plenty of room on the iTouch so that wasn't the problem.
We found this thread and she tried Lukeless's solution repeatedly, but couldn't hit the "pause" button in time (the 0.1 second that someone mentioned above seemed about right).
Finally she just started tapping repeatedly... not really trying to hit the pause button, just tapping it as quickly as possible. Dozens of times.
The song WENT AWAY. She panicked.
(I know we could have just tried to buy the song again, but I'd have hated to do so, on principle. Hate to pay them twice. And there was always a chance it'd fail the second time too.)
After a couple minutes... the song came back, and downloaded properly!
So maybe one of her taps paused and another restarted it, like Lukeless recommended. Or maybe she just overloaded the user-action queue, and that helped reset the download. Or something else. In any case, it worked.
Good luck.
Quick comments:
1. Come on, Apple, get on this. Really. Horrible user experience. The second-to-last thing anyone wants it to buy something and not get it... the *last* thing is when that unsuccessful download is fouling up the ability to download other stuff!
2. Don't assume the user's running out of room and that must be the error.
3. Don't assume the user can connect to a PC or Mac. That's not a solution! That's a workaround that might work for some people. iDevices are supposed to be able to download without being sync'd, that's inherent functionality.