With a variant: the babies don't just vanish, they disappear for a while, and then come back. But alas, inexplicably, once they're back they begin to age very fast.

Maybe they don't disappear at all, they just start to age and that's how the inquiry starts. People notice the disease and think it's some kind of virus; but a young journalist trying to connect the dots notices all affected babies stayed at the same clinic at some point.

He goes there to see for himself and is greeted by a brilliant doctor who's wise beyond his years...