It says that you can only use Baby Boost once or it will start to diminish. Does it mean once per family or once for the entire game? I have been giving each new set of parents a little boost. thanks.

You can give as many baby boost shots as you want (and can afford). What "diminished effect" means is that, after the first shot, each additional shot provides less of a boost than the one before it, but it still provides some amount of boost.