If you want it to last plant it in grass boxes, made out of 1x6's or 1x4's covered in hardware cloth. As it grows they can eat what comes up through the wire, but they can't scratch in it or pull it out. So it makes it kinda hard for them to kill. And you can just reseed it by tossing seed through the wire or if you want to can pick the frames up and move them to a new section of your run and start them over. Leaving where they were sitting for your new babies to completely enjoy.
I would use a pasture grass mix, it is a little more hard to wear and tear then regular grass.