Ideas
I also have this issue. It's much more frequent than the random bunny death, too. If a bunny dies, you get a notification and your sims get sad moodlets, in the case of random bunny disappearance, it's like the bunny never existed. The game then spawns you a new bunny, until your bunny home is full with its max 5 bunnies again. Then you get to keep your bunnies for a random amount of time, until one or two get deleted again and you start over.
I am pretty sure there was a bug report about bunnies randomly being deleted on here a while ago, but I can't find it now. I think in that thread the theory was that the game deletes bunnies if they are out of lot boundaries when you travel or go to the map. My main household lives on a 50x50, so lots of space for the bunnies to hop around on lot, but I have observed them off lot in the surrounding area, and they do occasionally just disappear/get deleted. Bunny loss is a lot more frequent on smaller lots (presumably because the bunnies are more likely to hop off lot and are then lost if you travel, which would support the theory they get deleted off lot). Bunnies aren't kept in by fences, they dig under them, so there's no way for the player to keep the bunnies on lot. If being off lot is indeed what causes this problem, maybe a fix could be attempted by forcing bunnies to not leave the lot?