What if Alex killed herself?
Then what would happen to the Djinn?
Tad: You're a mean old witch!
Sandi: I am NOT old!
Well in the second film, the girl who awoke the Djinn got shot and it healed right away like she couldn't die. I'm guessing the same thing applied to Alex. She was basically immortal until she either made the third wish or defeated the Djinn (which she eventually did). Kind of a lame explanation but I suppose it works within the universe of these films.
Horror_Metal