If the fairy story is for children then the answer might be different to a story for adults.
Fairy stories are often read to children at bedtime and a fairy being killed could lead to a sleepless night for a child and parents. Generations of children have grown up not wanting Tinkerbelle to fade away in the story of Peter Pan.
However if the fairy is in a fairy story adults and you really want to kill her off. . if it is part of the plot you need to check what purpose it serves. Also consider how and why you have her killed off in the story.... the only good of it that I can see is if she is saving someone or something important. Probably not much help but you must in the end write what you feel is correct for your story.