I'm having the exact same issue (cloud download icon disappears when tapped, no status / stop icon shows, and after a brief pause of 10 seconds or so the cloud download icon reappears). I'm using an iPad Mini Retina. It only appears to happen on iTunes U course videos. I am able to download PDF content associated with the course. One other note - it only began happening about a week ago.
I have two workarounds for the course I'm taking, that aren't ideal.
1) In the catalog there is also a 'collection' which is just the video series. I'm able to download the series. Unfortunately, the annotations and notes I've taken in videos show.
2) When I have an internet connection I'm able to stream the videos. Unfortunately this isn't ideal as I try to watch the videos on a commute. I'd rather not eat up cellular charges when I don't have too and it becomes untenable when the train I ride passes underground.