Ok, here's a theory:
It's not JUST that Takt is gay and has a politically important family that's trying to keep it quiet. It's that he also needs an heir for some reason. So given his... Condition... His family goes to the only girl he's close to that they can trust and make her an offer she can't refuse (offering to pay off a family debt, or help a sick relative, etc, you know the tropes).
At first she agrees, but then the weight of what they're doing sinks in. And she realizes that the way things are going, her first time will be to create a child in a loveless marriage of convenience. As much as everyone in the comments here calls her a whore for her behavior toward the MC, she realizes she has ACTUALLY sold her body as things stand, and doesn't want her first time to be a reflection of that. She wants her first time to be out of love, perhaps her last taste of a loving physically intimate relationship, before she has to spend the rest of her life cloistered away taking care of a child or children, unable to get away with having an affair anymore once they're married and have a kid.
So though she's not actually physically dying, for all intents and purposes she sees this year as the end of her life and freedom, and is acting out of desperation in response to that, despite being either unwilling or unable to cancel the deal she's made.
So she whispers to the rapist "Sorry, but this politically powerful family that can probably easily have you killed is counting on me to pop out a kid soon. But don't worry, I can probably sleep with you after that... if you still want to." Yeah, no wonder Roofie McFuckface backpedals real quick from that once he's realized he's potentially messing something way out of his depth, when his goal was just to fool around with a cute girl whether she wanted it or not.