This happened to me too today, this problem seems to still exist in iTunes.
Here is what happened:
I rented Nightcrawler from iTunes and it was downloaded and I started watching it.
During watching it iTunes crashed. I restarted iTunes and the rental was gone. I was able to find from the iTunes temp folder a file download.m4v and Info.plist. Music/iTunes/iTunes Media/Downloads/Nightcrawler _ Dan Gilroy.tmp
I thought that maybe I will add the download.m4v to the iTunes and maybe it plays me the movie. Did not work, instead iTunes said that "This computer is not authorised to view this movie" and it deleted the file immediately without even asking. The nasty smelly ugly DRM stuff takes its toll.
I checked the support option schedule a call, and it offered me a slot for call for next Monday. I was wanting to watch the rented movie TODAY, not sometime next week or later. So I chose the email option for the support.
During the time when Steve Jobs was still alive and the CEO of Apple, I needed Apple support once. I contacted them via the support (the email option) when I had previous time problem with iTunes (long time ago) and some very polite and helpful person contacted me within the next 15 minutes, and he not only contacted me, but he was able to promptly solve my problem. I was very positively surprised.
Now I was thinking that maybe a helpful person will reach me in the next 15 minutes like in the previous time it happened, and my evening does not get ruined and I can continue watching the rented movie. Instead of getting the real person contacting me promptly, I just got automated reply that they maybe answer me during the next two days or so. So my movie evening got ruined by Apple :/ Where is this nice support person who was eager to help, is he gone nowadays, is he or people like him anymore working for the company at all?