These problems of slow downloads have been going on for YEARS and Apple does not seem to care. They just say that Apple TV is a "hobby" and laugh. I was given a first-generation Apple TV as a gift in 2007 and I have always had movie streaming/download problems. Apple iTunes Store support were always very nice and tried to help, but the problem was outside their control; it was apparently caused by incompetent planning and design and/or ignorant/cynical cost cutting.
The manifestation of the problem I see is:
(1) Movies download at about 1% every 1 - 2 minutes, but with significant variability. For most full-length movies, this means that at least 50% of the movie must be downloaded before starting to view it, if interrupted viewing is to be avoided.
(2) Apple TV tells me the movie is ready to view after only about 6% has been downloaded. From (1) above, it is clear that this is hopelessly wrong. If I start viewing at that point, the movie stops within 30 minutes as its download cannot keep up with the viewing rate. Being given this patently untrue message just adds insult to injury, and makes clear how hopelessly messed-up the design of the overall Apple movie-viewing system is.
I have given up on Apple; they should be releasing wonderful new products to augment TVs, beautifully designed by Jon Ivey, and with true ease of use and dependability built in, but all they have given us is two failed versions of Apple TV.
My advice is to start downloading AT LEAST two hours before you expect to start viewing. Apple has had years to fix slow download problems and has chosen not to, so don't expect anything to change.