Sometime around mid January in the game my people stopped feeding the small pen of rabbits I had built. There was no lack of food as I had 400+ simple meals and a thousand or more various other raw plant goods that I had seen them use before. It got to the point where I set all my guys up to just do handling and still not one would feed the four starving hares, and it's not like the door was locked or anything. So I got annoyed and blocked off the freezer with walls then shot the boomalops outside my power plant and watched everyone die in the cold of winter. I was less than pleased.
p.s. I don't know how you'd go about replicating this issue.
handlers don't feed your animals, except to tame them or train them. After that the animal is on their own to eat.
All you need to do is put a stockpile inside the rabbit pen, and the rabbits will feed themselves. since they are herbivores, stock it with hay, or any other veg.