I don't think the pregnancy problems began with the Incident. If it had, you'd think Dharma would have done some research on why their pregnant women were dying. Richard Alpert probably wouldn't have been so dismissive of the problem if it had lasted thirty years. If Ben's ascension was the catalyst, I'd imagine the other Others would have noticed ("hey, Ben takes over and our pregnant women start dying---wonder if they're connected??"). So what caused babies to stop being born on the Island?
I think it ties into the MIB's imprisonment. We know he was walking around freely in the 1800s. He was presumably imprisoned sometime after the cabin was built (so sometime after the Incident). But Jacob was using the cabin for a time---otherwise, why would Bram/Ilana bother looking for him there? So the MIB's imprisonment should be relatively recent.
Here's my theory: the MIB had a child. Jacob then had him imprisoned in the cabin, and the child was sent off the Island. The MIB then went into a furious rage and vowed that no children will be born on the Island until he was reunited with his own child. (Everyone on the Island has daddy issues/caused daddy issues---why not the MIB?) Shades of Sawyer/Clementine, perhaps?