I'm not saying they need to have kids, but are they actively avoiding having them? Is she drinking some sort of contraceptive tea? Is she infertile? They have been going at it like bunnies, and still no baby.
Given the time and the fact that he has a title, he needs an heir (part of his responsibilities), this has never been addressed (i think one chapter touched on the fact that a friend of hers had been married for like a day and was already pregnant, I could be confusing this with another story, who knows).
Ignoring the unrealistic fact that tea can solve every issue known to humankind; that a Duchess can get publicly drunk and the entire aristocratic society laughs it off like "oh gosh, that darn Duchess at it again"; that the main plot of the story and what was plaguing the FL with worry was solved 1-2 chapters...how is it that this has not been addressed (be it that they don't want kids or that she can't have them or that he's infertile) or that noone else from that misogynistic society (if i see one more shocked faced at the fact that the FL actually has a brain, i will have a stroke) has not addressed it?
Besides a meme face on every other panel as a gimmick, has there been any progress in the story or plot? Or is the story just a collection of meme faces?