Yes I have had a weird occurance like that too, where I found an invincible hare that when I hit it with an arrow I saw it bounce off and go 5 blocks away not killing the rabbit.

I have also had the same exact problem. On my personal server the rabbits run away at a distance they shouldn't, I know that because on my friends server the rabbits act normal. I have no idea why they do this. They are always running only stopping for 3 seconds then running again!