Daenerys was born nine months after her mother's flight from King's Landing at the end of Robert's rebellion.
She had been born on Dragonstone nine moons after their flight, while a raging summer storm threatened to rip the island fastness apart.
That means she was conceived around the time of sack of King's Landing. For a defeated, mad old man awaiting imminent death and a woman in immense stress, this would be an unusual time to conceive a new child. Besides, many misfortunes could have befallen the fleeing Queen Rhaella during her flight to Dragonstone that might lead to a miscarriage.
Is it possible we are looking at another case of pretended parentage like Jon Snow's, or is Daenerys's unusual conception at the conclusion of rebellion just a coincidence.