Hi - We have a rabbit warren at the end of our garden. When the rabbits were first a problem I wire fenced most of the flower and vegetable beds. Eventually we found the only way of dealing with the rabbits was to dig a trench around the garden and sink chicken wire (or similar) in an 'L' shape into it. Our gates are also covered in the same, and hung so there is minimal gap at the bottom. However, where we have a hedgerow and trees down one side we still have a chicken wire barrier but it is only pegged at the base. Along some parts of this wire fencing the rabbits did get through and caused havoc. We eventually found we were filling in their holes with concrete and that has worked so far. We don't have a rabbit trained dog, but this might be another option.
As much as we love gardening, it often seems there is something trying to challenge us...