Guys, I have developed a theory of a bunch of stuff on the Island and it might not be right and it's also not based on any future spoilers or anything, btu I'm making i tiny print anyway in case anyone cares to read, but it's cool if you don't.
Okay, we know that time spent on the Island = quicker deterioration of the body when jumping.
What this says to me is that there's a sort of energy radiating from the Island into the people on it. The more energy you absorb, the more of you is on the Island's time. In other words, when the Island jumps, if you have enough timey wimey stuff absorbed, you jump with it. But if you don't, you get left behind. However, the more timey wimey stuff you've already absorbed, the more of you actually does move with the Island in its jumps, thus killing you quicker, the longer you've been on the Island.
Okay, so that brings us to the Oceanic Six. There were 8 people on Ajira Flight 316 previously on the Island and four jumped with the Island to its own, newly reanchored time while four were left behind. Lapedus, obviously, had spent barely any time on the Island, so he clearly must not have had any energy to jump. Ben and Locke, meanwhile, has actually activated the anchor and been shot through time, possibly cleansing them of their built up energy. Sun, however, has been on the Island as much as anyone else of the Six. So why didn't she jump?
Because she was pregnant. Ji Yeon absorbed the Island's energy, not Sun. Once she gave birth, Sun was practically off the Island's time, because her child had taken it. So she didn't get to go back in time with the rest of the Six.
Which, then, obviously leads us to why children can't be born on the island: they're being poisoned by the Island's temporal radiation...stuff. Ji Yeon survived by being removed from the Island in time, Aaron survived by being off the Island for most of development, but any other child is screwed.
And all of this energy being released and poisoning the Island's inhabitants must clearly be new, since children can be born in 1977, probably a result of Dharma's messing around with the Swan and whatever incident occurred.