Of course they do. Do not panic if your rabbit does not sleep for a long time. In fact, they are still asleep, just the owners of ornamental rabbits do not notice this, and if they do, they do not betray it. In general, decorative rabbits are nocturnal animals, so they prefer to sleep during the daytime and at night to stay awake.
It is quite natural and with time you will get used to it, and if not get used, then humble yourself.
It is necessary to know that ornamental rabbits are very shy animals. They can even die of fear, for example, from loud noise, so you need to take care that nothing and no one scares your little beast.
The eyes of rabbits are almost always open. When they sleep, they do not cover them completely, but slightly screw up their eyes. It is normal for these animals to sleep, with their eyes open.
Rabbits can be hammered into corners or fall apart in the middle of a cage – for each rabbit it is individually. He can slightly doze and wake up from every noise, and can sink into a deep and prolonged sleep, like people.