Why can't I transfer this video to iPod?

Recently I had to restore my 4th generation iPod nano and am uploading music back on to it. I have a music video that I bought in the iTunes store. It will play in iTunes just fine, but when I try to transfer it to my iPod, I get this message, “____ was not copied to the iPod because it cannot be played on this iPod”. I have tried going to Advanced > Create iPod or iPhone version, but that option is grayed out. I am really irritated that a video from the iTunes store will not play on my iPod. How much sense does that make? I cannot re-download the video from the store because it is no longer available. What else can I do?