Why is it impossible for women to be impregnated on the Island and survive the whole pregnancy?

It was never directly addressed on the show. However, Damon Lindelof and Carlton Cuse have hinted on the podcast that perhaps the detonation of Jughead during the Incident had some effect on pregnant women on the island. Hence, we see why Ethan was conceived and born there without problems, while many others died in the middle of the term.

In the epilogue "The New Man in Charge" during the part in the Dharma factory where they watch the orientation video about the Hydra, Pierre Chang says that the polar bears working at the Orchid station may experience pregnancy issues. This suggests that perhaps the island power source itself (a part of which formed the power behind the Orchid station) caused pregnancy issues, perhaps at will, perhaps randomly. Maybe this was intensified by the detonation of Jughead? We may never know exactly.

One must not forget that Jin and Sun conceived on the island, and Sun gave birth off the island. For that, and the fact that the creators have stated it clearly, they were not dead the whole time, this rumor must end.