EDIT: I just had another idea. I saw what I believe was a long-tailed weasel, today, and its droppings. Ahem. After researching to find out what I had seen, I discovered that they eat rabbits. Then, I learned that ferrets eat rabbits, too. Ferrets are often pets. They have a strong smell. The smell of ferrets is said to stress rabbits out.
My idea is to get some urine of a rabbit predator (fox urine should do the trick), and put it around your yard.
We had a surplus of large, white rabbits in our neighborhood once. This was a rather unexpected experience, to see three large white rabbits investigating our front yard out of the blue (multiple times). We came to find out that someone up the street was raising free range rabbits. I think they started as a 4-H project, but there were almost 45 at one point. I only ever saw three or less at a time in our yard. They were around during the fall (a couple years ago or so), the entire winter and part of the spring. Then they vanished mysteriously.
We had children in the neighborhood who were always trying you catch the rabbits. Apparently, they seemed to be fairly successful, but there were still rabbits notwithstanding.
My other neighbor trapped a few, and put them in his freezer.
By and large, though, I think the hawks and coyotes got them. After the snow melted (and they were no longer camouflaged), they disappeared pretty fast. I don't know how they survived so well before the snow came, though. They were a lot faster and more suspicious after they'd been free range a while.
So, if you can attract hawks, that might be a good idea. Maybe that's easier said than done, but some people do put up perches for them and stuff. I don't know if you want coyotes; I hear they eat some garden fruits. Maybe train your dogs to chase rabbits.
Lately, there have been chickens in our neighborhood instead. Perhaps this is a trend.
Anyway, rabbits don't tend to climb high, normally. So, you might consider gardening higher up, if this turns out to be a chronic problem.
You can have plants that climb trees (like Kiwano, Shark Fin Melon and stuff), and then you only need to protect the stem.
I haven't tried it, but you might consider something like hog wire as a border; perhaps it would work if you get a kind where the gaps aren't too big. Chicken wire has smaller gaps. I've heard it can work. You can line a sturdier fence with it.
Here's some discussion on the problem. It may be helpful.