Do/can rabbits sleep with their eyes open? I know this is a really weird question but I think Toby does sometimes. I use to think he was awake and could see everything going on (even though he looked comfy for sleep) but in fact when I have opened his cage it has looked as if I had woken him up - though his eyes where already open lol. Toby does tend to sleep during the day and wake up ay about 11/12 o clock.