Why can't I download a movie from my iTunes Library to my iPod 4G?

I just bought a HD movie from iTunes, but when I tried to download it to my iPod, it would recognize that the movie was on my iPod, but the movie woudn't be in my Videos App on my iPod. So then I redownloaded it in SD, and I tried syncing it to it again, but still it would not show up on my iPod. Yes, I've tried redownloading it several times, I've tried updating my iPod and downloading it, I've deselected the movie and then reselected it, I've tried both HD and SD, but nothing has worked. Am I not looking in the right place on my iPod, or is there anything else that I can try? By the way, I have the most recent version of iTunes and it doesn't give me the warning that my iPod can't play the movie. It doesn't even give me the option to make it compatible, if that's the problem. PLEASE HELP ME! I've been working at this for two days and have tried everything I can think of or have seen on the internet. Please give me some suggestions on what to do, or at least tell me if you have had the same problem so I know it's not something wrong with my computer. 😟