I've never had a rabbit I shot come back, at least not yet. If it happens I might consider moving...
As mentioned, a fence works well, especially if one buries it a bit underground. For my wife's first garden I took 4' tall chicken wire, folded it in half in an L shape and buried the one half a few inches under ground. Going out 2' was enough to keep the rabbits from digging in, especially after adding some mulch over the top to make it all look better.
As we got older, I made tables for her to use for her gardens. Now, the soil is waist high which makes easy what little weeding needs to be done and there is no bending over to pick veggies. Tomatoes can be a pain if a tall hybrid is picked but she has learned along the way. I made a deep planter so she can even grow carrots which are tough in the pottery clay soil we have.
I know others who have built raised gardens but I like the benches I made. There is no bending over which is becoming more difficult as age rushes up on us. The only drawback is using cedar and not treated wood as the preservatives can leach into the veggies and potentially cause problems. So far the beeches have held up well, the oldest is 6 years old and has no signs of rotting yet. The wife uses potting soil and other additions and it may be that it does not hold water and other organisms to cause rot like top soil.
