The giant statue, who is most likely Tawaret at this point, possessed some kind of power that allowed women to give birth on the island. This makes sense since Tawaret is the goddess of childbirth and fertility. However, the statue lost most, if not all of its powers when it was almost completely destroyed. Possibly the foot of the statue still possessed some power and that is why Claire was able to have Aaron after a lot of effort??
Also, we can put the statue's destruction sometime between '74 and '04 because Amy was able to have Ethan, and also because Sun had caught Ben in a lie when he tried to say that it had been destroyed before he had come to the island, so that means it was there in the 70's.
Could the incident/hydrogen bomb have caused it's demise???