Ok, as I said, I was not sure and it's just what I found, but as the other said, the story is about curing her for good, and for that, you need to finish the first "great adventure" during the weekends. This makes sense. So probably, if you wait for too many days to do so, then she dies even if you take care of her in the evenings when she is sick.
It was not a bug then, I just didn't read enough. It's probably not a quest that requires to rush (at least if you play with the normal difficulty), but you need to do it.