Both died withing a couple of weeks in between. I told this before also. Please see Abhay's historical posts. They need not have died naturally. Read Abul Fazl's account of how he says about twins death. Its mysterious.
Even in the show, if you notice, they showed the audience of how Zeenat poisoned. But, none in the Empire knew of this. May be thats why truth was permanently hidden. Not only that, in the twins one could have died naturally and the other like this too. May be Akbar comes to know much later about this poisoning, but, he may have protected the identity of the people involved as it was by his own relatives, so he may have never allowed his official chronicler Fazl to let the truth out.
If you see later history too, Jodha never delivered her babies later on in Agra fort. It happened outside only, as far as I could deduce. There were couple of daughters born of which one didnt' survive, then the next survived, i think it was Jahangir's beloved elder sister. Then, both JA went to Salim Chisti on pilgirimage wanting a son - a heir to the throne. There, Jodha lived in that small hutments of Salim chisti's hermitage and delivered Salim. I think Akbar saw his son only after 45 days of vrath or something coz, he was told by his maulvis, may be Chisti himself not to see the child as soon as he was born, "nazar nahi lagna chahiye" of the father - some such beliefs or as per some astrological calculations, in those days.
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