I was out for a walk Saturday evening in the dark and I use a flashlight when I'm walking in the dark. I swung the flashlight over to a front yard and saw a rabbit scurrying into some brush and it stayed there for a while. I see rabbits in Southern NH once or twice a week when I'm out for a walk or running around the neighborhood.

We have a partial ownership of a place in a Boston suburb and there are rabbits there too. So many that someone's WiFi router name is rabbits. I'd guess the reason why you have or don't have rabbits is the number of natural predators.