Na; early on it did a bit, then I realized I can just reread it and the character will be back. If the story is well written the death will improve it, and if it's not I probably won't care about the characters anyway.
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That’s an interesting way of looking at it. I thought the same too until I read one fanfic once (forgot the title atm)
But it did a really good job of hooking the character and making him endearing to the point that I mourned his death a little.
It no longer bother me as much as it used to, but when I started, some deaths also keep me up at night to the point of writing my own fanfic to a fanfic just to give a character a happier ending. :)
Sometimes it does; it depends on the character and how they're written. If the character is well-written, I'll definitely be bothered by their death, but if not, I won't really care.