I think anybody who builds a rabbit hutch needs to be aware that the wood, wire, staples, etc. that we build with really only keep the rabbits in; any seriously interested predator would get through any type of hutch or cage in a matter of minutes. Some materials (like particle board) even the rabbits themselves will chew through.
I use 16-gauge 1"x 2" welded wire and 1/2" plywood for the sides, and I have had hutches "breached" by dogs - if they have time (like at night, while the owner is asleep) they can pull and chew their way in. A dog with a high predator drive will do it. Even if they don't rip their way in, they will bite at the rabbits' feet from underneath the cage; many rabbit owners have had rabbits lose toes and even their lives from this sort of slow torture (take my word for this, I've had it happen, and it's horrible). A hutch by itself won't protect your rabbit, you need a further level of security (a fence or building) to keep larger predators away from the hutches.
Nope so far none of them have even chewed on the chicken wire as far as I know the biggest problem I have had is with the salt wheel in the cages. When I clipped it on the side of the chicken wire it started rusting the wire within a week. But to fix that I just ran some bailing wire and hung out from the top of the cage so it wasn't in contact with any of the cage wire. It worked good. Although I'm starting to wonder why I even keep it in my does cages they hardly touch it where as my buck has gone through 2 and is working on his third one since I got them back in June.My rabbits do that too! It is SO ANNOYING.
Have you had any problems with rabbits chewing through chicken wire?