When was it ever stated that the bomb going off caused the infertility problems? I don't recall that ever being mentioned in the series (or in most interviews I've seen).
I think that's just logical. The radiation would have had an affect on reproduction. (I'm thinking back to the long term effects from Hiroshima and Nagasaki).
It was the reason for all the concrete in the hatch that, as Sayid noted, reminded him of what happened at Chernobyl.
Ahh... But I don't think that makes sense in this situation.
First (and primarily), the effects of long term radiation exposure on fertility is quite widely known and studied (and has been for decades) to assume that the Other's (and especially a world leading expert in fertility like Juliet) would not know about it, be able to detect it, treat it, etc... is simply to silly to accept. It would be one of the first things they would look in to, especially if the problems starts soon after the Incident and since they knew they had nuclear material on the Island since the 1950's. Maybe if the Other's had ended up all being backwoods hicks it might have made sense, but they had scientific experts, access to off island resources and scientific know how, they ran that Biowerk(?) medical company that hired Juliet and had the big secret high security compound, etc... If it had been simply radiation fall out causing the fertility problems then it would have been easy to diagnose.
Second, radiation effects the reproductive systems of males and females by lowering fertility (low sperm count or defective sperm count, defective eggs, and the like) that is not what was happening on the island. On the Island woman could still get pregnant. They died after months of carrying the child, usually during childbirth. That is not something that radiation poisoning would cause.
Third, and this is more my take on the "Incident", but I still do not believe that they actually detonated a nuke. The nuke (and any nuclear bomb from that time) was huge. Sayid used Daniel's notebook to take out the primary explosive device of the bomb, but not the full nuclear bomb itself. All I think they detonated was an explosion at the location of the unstable energy, causing a massive blast, but not a nuclear explosion.
To assume that they could strip down a 5 ton nuclear weapon, in an underground cave, with limited tools, using a old notebook, by torch light and still end up with a working nuclear bomb that someone could run around with and carry in a backpack is a bit too outlandish even for Lost. Daniel said they were going to use the nuke to blow up the energy pocket, but he never said that it was going to be a nuclear explosion that would do it. It was just a source of highly explosive material that they had access to and that he knew would be there to use (remember he was living/working in the 1970's at the time he came up with the plan and he wouldn't be able to transport any high explosives back to the Island so he would have to work out a plan that would make use of materials he knew were already on the Island when he returned. And he wouldn't know if they had any other source of high explosives on the island except for the bomb (that he had studied before in the 1950's))
Fourth, If it had been a nuke that went off at the Swan site then people living there (like Desmond, The Losities, etc...) plus all of the animal and plant life would also have lots of problems. Putting all the concrete down would stop further contamination but it would solve all the problems of what would already have been released in the blast. Chernobyl is still a no go zone 20+ years after the meltdown (even with all of the concrete) and will be for decades more. And that was just a nuclear meltdown, not s full on nuclear blast. Also there would have been a
major blast zone/crater if a nuke had gone off. That is not seen around the Hatch. The jungle looks normal. Old trees, normal plants and animals, no crater radius or anything like that that would show a nuclear weapon detonated in the area 20 years earlier.
So... With all that I do not think the "Incident" was a cause of the fertility problems.
The cause had to be something that a world expert fertility doctor, that had previously made a barren woman pregnant, could not find the answer to (or even the cause of). Radiation would not be that cause.
A much more likely answer would be that either Jacob or more likely the MIB used their powers to prevent children from being born of the Island. Maybe to stop a population explosion on the Island? Maybe so no other children would go through what they went through growing up on the Island? Or some other reason like that.
That would be why no one, even experts, could find the cause or cure for the problem.
