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

The Island somehow strengthens the immune system of people on it, and provides some other healing capabilities. The issue with pregnancy, which I think Juliet explained, was that the amped up immune system mistook pregnancy for a disease. The immune system would interfere with normal pregnancy, resulting in a miscarriage. People who got pregnant off-Island would not have those complications, and by the time the Island's effects kicked in, they would give birth.

Electromagnetism.

The series epilogue The New Man in Charge explains that the Island's electromagnetism damages the mother and baby during the first part of the pregnancy.

Dr. Chang: Affix this tracking device around the subject's neck. At which point it will be transported to the Orchid station for the next phase of research. Remember, be sure to confirm that the female bears have not been impregnated before transport, as the electromagnetic levels at the Orchid have an extremely harmful effect on early term gestation.

This also explains who Claire was able to give birth on the Island, as she had become pregnant off the Island, months before.

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.