Breeding like rabbits

A while ago we took one of the bunny girls to visit a friend's male rabbit. The gestation period for a rabbit is about a month. We felt her belly a few times to see if we could feel any growing little babies. We couldn't. We waited the full month though because apparently it is sometimes hard to feel them even for rabbit breeding experts.
5 weeks later when we were sure there was no success Doug put her back in with our male rabbit. Previously he has had no idea what to do and has cowered in a corner while she harassed him. This time roles were reversed, he was super keen - but didn't seem to know in detail what he was supposed to do, but gave it a go anyway. She cowered in the corner with her tail tucked under her. Doug thinks that given this and his misunderstanding about some of the mechanics involved that it is unlikely she is pregnant.
Where did the phrase 'Breeding like rabbits' come from. In our experience this would result in the race dying out...