Some of you have been introduced to my bunnies, Brown and Grey…

…who live in a play area, which is actually a big first floor balcony in my house. See Link to YouTube
Right now I put the rabbits in the cage and close them for the night and cover the cage with a big cloth to protect against cold draft. Apart from those 8-12 hours, the bunnies have full freedom. I was wondering whether I should just keep the cage open 24/7. It is a bunny safe environment and they have hiding boxes and tunnels to protect against draft.
We do have lots of stray cats running around our house though, even during day time. A bunny was taken away in the past, before the above two, but it was very sick and not moving when it happened. While it was taken away from a place other than the play area, I have myself seen cats walk close to or the outer wall of the balcony/play area.
I guess Brown has grown really strong and big to be a prey. Grey perhaps not much, but she is always hidden in her box, and only comes out to eat or run around.