Hard to figure out the characters at times. The king knows she has an incurable, debilitating, painful, deadly disease. He knows she knows and has accepted it, and is pretty much over the whole political game, since there's no long term for her to plan for. She just wants to bow out and spend her last few years peacefully away from the public (only she knows that she won't actually die, or that she doesn't actually feel the pain she should be feeling). And yet, when she wakes up after fainting for three days, as a result of said debilitating, deadly disease, he's shocked that she treats it like nothing. What kind of reaction was he expecting? She knows she's dying, and spending a few days in a coma is part of it. Why would her disease progressing in increasingly visible ways lead her to change her position of wanting to leave? Things are simply progressing in the way she predicted they would, which would naturally only reinforce her beliefs. And he hasn't given her any reason to reconsider.
It's like they just react in dramatic fashion, even when it goes against what they should already know. Also, not surprising that the prince was interested if the other person with a claim to the throne is developing some kind of disease. Especially if she faints for three days straight, and he hasn't been told that she is dying, or that she wants to give up her claim to the throne and it is only the king wanting to ensure her safety that is delaying her.
Also, I'm surprised by how little we've seen of the king so far. He supposedly delayed her because he felt guilty about how he ignored her, but he hasn't made any effort to pay attention to her since.