My daughter has asked for help from the Teeming Millions.
She reads a number of Manga series (they all look alike to me). She has noticed that whenever she decides a given character is her favourite, that character is killed in the next issue.
She is looking for a term to describe this, or a “law” that she can quote on her message boards.
Any ideas?
I have yet to hear it referred to by a specific term less vague than curse, but it is a very very common phenomenon in any series about anything. If no one else comes up with something we should.
I’m leaning towards “Martinization” as in George R. R., or something similar.
The Mercutio gambit or curse of the fangirls?
I’m gonna go with good ol’ trusty Confirmation Bias.
Bad luck.
Character Assassination? 
Name it after your daughter. She’ll be famous!
The Hal Jordan Principle.
No, that would be the principle that there is no character change so drastic that it can’t be fixed (and excused) later through major retconning. Formerly known as The Phoenix Principle.
I don’t know but it happens to me with makeup, too. As soon as I find the perfect lipstick color, it is discontinued. Always.
It would certainly explain why According To Jim can’t be killed.
I can’t think of a specific name for it,* but if anywhere, TV tropes probably would have it classified.
*A certain corollary of Finagle’s Law would seem to apply, at least in part.
Hmm. I’d call it an article of Murphy’s Law. But then, I blame almost anything on Murphy’s Law.
Whedon’s Curse?
No, because often (especially in anime) the reason you started to really, really like them is that they suddenly got a lot more screen time and backstory. Call it the Nuriko Effect.
Presumably this is a reference to Nuriko in Fushigi Yūgi.
Of course, there are plenty of manga and anime where no one dies. And there are cases where a major character is already dead at the start (e.g., Fujiwara no Sai, who died about 1,000 years before the start of Hikaru no Go).
Bravo.