In addition to Game of Thrones Season 7 moving at warp speed, fans may have noticed that this year's writing is ever so slightly heavy-handed. For example, it was brought up not once but twice in "Beyond the Wall," that Daenerys can't have children — first, in an exchange with Tyrion about who her successor will be, and later, when she tells Jon Snow that her dragons are "the only children she'll ever have." So why can't Daenerys have children on Game of Thrones? It goes back to a maybe-prophecy/maybe-curse from Season 1.
Remember that Daenerys has been pregnant once before, with Khal Drogo's son. When Khal Drogo suffered a terrible wound in battle, Daenerys insisted that a godswife and maegi named Mirri Maz Duur treat him so that he could hopefully be healed. He agreed, in spite of warnings that this woman dealt in dark magic, and sure enough, Drogo's wound festered and he wound up on the brink of death. Desperate to save him, Dany told Mirri Maz Durr that she may perform blood magic on him to save his life. She forbid Dany from entering the tent while she performed the ritual, but Dany walked into it anyway.
What came after was nothing short of tragic. You see, what the woman failed to tell Dany was that in order for Drogo to survive, it would require a blood sacrifice: the life of their unborn son. She ended up losing her baby and even when she did get Drogo back, technically alive, he was left in a vegetative state. When Daenerys asked Mirri Maz Dur when Khal Drogo will return to normal, she replied:
When the sun rises in the west and sets in the east. When the seas go dry and mountains blow in the wind like leaves. When your womb quickens again, and you bear a living child. Then he will return, and not before.
Dany interrupted this to mean never and that she must be barren. It's not clear whether Mirri Maz Durr's words are a prophecy or the curse of a witch who resents being enslaved, but either way, Dany obsessed over this during the course of the books. Incidentally, the books also describe Mirri Maz Durr giving Daenerys a mysterious drink that tastes like "sour milk, and something else, something thick and bitter" while she was in labor. Later in the books, Daenerys ate bitter green berries which she thinks taste familiar and then apparently has a miscarriage. So some book readers think Mirri Maz Durr sabotaged Dany's pregnancy by poisoning her with some sort of natural abortifacient.
Either way, the Mother of Dragons is definitely able to conceive. She just hasn't been able to successfully give birth yet.