Hmn. For me it depends. In this case i wanted her to live cause i really liked her character.
I was rooting for her.
So seeing her go through all that only to die when she didn't deserve it was...ouch.
There are other times tho where no matter how much i like a character i can still recognize that they deserve to die, and in those cases deus ex machina can be incredibly annoying
It's not that I accepted that someone dies because they deserved it. Good people, bad people, they all die at some point. Even if the ending wasn't seen they still die in the background unbeknowst to the readers. But I liked the fact that she dies because the way it was written, the author embraced mortality. A lot of manhwas/mangas/manhuas/webtoons are centered on the "Power of Love" where they unrealistically turn out alive when in logic they're supposed to be dead-- basically the logic of fiction (which is also a defense in your case). Anywho, I love how unique it turned out. Even though it's a sad ending, I love how they didn't forget that she was still terminally ill. Well, that is also a major plot point so I doubt it'd even be forgotten. (=・ω・=)
Oh, and in this case it's not really deus ex machina since her being terminally ill is already a given from the start. Except if there was medicine for it, it should already be known from the start that she dies. Especially since this is the old times and not much development regarding medicine has been made (as far as I know).

Hey guys according do spoilers she dies in the end :)