Dee sleeps with her eyes closed when she's flopped on her side on the floor or in her cage. If she's sleeping in bed with me, she does the eyese half-closed thing mostly though I can't say for sure about all of the time because she burrows under my covers. Of course,this is the bunny who bites my dog and anyone stupid enough not to pet her when she jumps in their lap. (She gives a one grunt warning that you shound begin petting and if you don't, she bites - she has us well trained.) She's not afraid of anything that I've found yet; no survivial instinct but that's okay 'cause I'll protect her.
Shadow - I've had her for 4 years and I'm not sure she sleeps at all ...I've never seen her with her eyes completely closed. I've only seen her eyelids droop when her and Dee are in the cage and she's laying between Dee and the cage wall.
It's a full house...
Munchkin - my 7-year-old human child who is much more work than a pet
Casper - my fluffy mutt with a shady past
Dee - my angry destructive wonderful bunny
Shadow - the bunny who lives here and is devoted to Dee but only likes sleeping humans
And the Ratkins - Blaise, Tersa, and Aura