An exposed garden — no trees, no nearby buildings, open sky — is hunting ground, and a rabbit run in the middle of it sits in full view of every sparrowhawk, buzzard, and opportunist crow passing over. Rabbits know this in their bones; a hawk's shadow crossing the grass sends them bolting for cover that may not exist. The cover over the run has to do two jobs: physically stop a bird reaching the rabbits, and give the rabbits darkness to dive into so panic itself does not injure them.
Why loose netting fails both animals
Soft netting thrown loosely over a run is the commonest cover and among the worst. It sags between its supports, so a bird striking or landing presses it down towards the rabbits rather than being held off by it. Its strands can entangle the talons and wings of the bird itself, leaving you with an injured, thrashing predator inside the cover and rabbits scattering beneath it — a danger to every animal involved, including the protected species you are not allowed to harm. Loose edges lift in wind, opening gaps at exactly the corners a crow learns to work at. Netting is not ruled out, but only netting installed like a structure, never netting draped like a cloth.
The cover that works: rigid first, netting done properly
The strongest answer is a rigid roof — welded mesh panels or solid sheets fixed to a frame — which no strike can deflect and nothing can tangle in. If the run is large, roof the whole thing in mesh panels and add one solid-roofed section. If netting is your material, treat it as engineering: choose a strong, fine-gauge net that a talon cannot slip through, stretch it drum-tight over a raised frame so it holds clear height above the rabbits, fix it at close intervals along every edge, and double it over the side facing the most open sky. The tightness is the protection — a taut net holds a bird off like a trampoline's surface, while a slack one wraps and traps.
Edges, fixings, and the shelter section
Covers fail at their borders. A bird that cannot get through the roof will test where the roof meets the walls, so overlap cover and sides, fasten down every corner, and leave no flap for wind to worry into a gap. Inside the run, build the solid shelter the cover cannot be: a roofed box or solid-topped section, big enough for all your rabbits at once, positioned so a bolting rabbit reaches darkness in one dash from anywhere on the grass. A rabbit that can vanish under solid cover stops running; a rabbit that cannot may injure itself against the mesh in its panic, which is how runs with perfectly intact covers still produce hurt animals.
Habits that back the cover up
Covers are the last line, not the only one. Site a movable run near the house or beside a fence or hedge rather than in the centre of open lawn, so the sky above it is partly broken and your own comings and goings discourage watchers. Supervise at the hours birds of prey hunt most actively in your area, and keep free-grazing sessions outside the run for the times you are physically present. Check the cover after wind and weather the way you check the sides — fixings loosen, branches fall, and a cover inspected is a cover that still exists. Mesh gauges, panel types, and frame designs involve several judgement calls, so put a follow-up question to KinsLe's Kimmy; she answers using the KinsLe Answers library.