I keep my bunny inside, but we have problems here with crows too. They attack our waterbags for the pool during the winter.
What we were told to do, which works pretty well, is cut strips of theshiney metallic wrapping paper (the kind that looks likethesmooth foil like they usefor theheliumfilled balloons), space them out & tie them on a rope (makesure the strips areabout 5 inches wide & long enoughto flap around a bit if its windy)& place it in youryard, preferably a few inches above the ground so the strips can flapin the wind. Apparently, the crows do not like the metallic color orreflections it gives off. It doesn't keep them away totally, they stillfly over head, but it keeps them from swooping down.
Usually what we do is take 2 garbage pails, put one on either end ofthe pool & attach the string that way, keeps them away from thepool. I don't know how your cage set up is but maybe if youcould put wooden stakes on the ground by the rabbitshutch& just attach the metallic paper onto the stakesthat way, it depends on how you have it set up. You can also put itaround the perimeter of the yard, that might help as well.
~pam