I don't have rabbit issues, so I am sorry I can't help, but if they can, a short fence of chicken wire on the outside top would keep them out, particularly if there is also some mesh several inches below ground (put in when building) since they can dig.

You might ask on the veggie garden forum.

Last fall, someone thought our house would be a better place with a bunny in it. So I spent half an hour trying to persuade the bunny that it really was better outside, and the someone that he should leave the bunny alone, and stop picking it up and carrying it further inside. The only thing that made any of this remotely manageable was that the bunny was surprisingly bad at vertical leaps. So it couldn't jump up on the furniture, and had to stay within my improvised corral funneling it back outside. Now admittedly, this was a small young bunny. Someone wouldn't have been able to carry around a bunny almost his size. But when someone was that size, he had no trouble jumping on beds, couches, tall bookcases ...