I think twilight managed to gain such longevity partially simply because it became such a big thing but mostly because it managed to hit on a teenage girl fantasy. I think it definitely appealed to other people as well but mostly younger women as far as I know (correct me if I’m wrong). We have so much vampire media because we’re fascinated with them. They’re sexy and dangerous and people like both. Look at how into serial killers people are, that danger is exciting.
So now you throw a teenage girl into the mix. She’s new to a school in the middle of nowhere and she gets noticed by the hottest guy in the school, then she find out he’s a sexy vegetarian human drinking monster but he won’t hurt her. And then still there’s a love triangle between a sexy werewolf guy thrown in there too with lots of sexual tension and situations that force Edward to shed his cold aloof persona and prove to Bella that he loves her. What teenage girl wouldn’t want to be Bella in this situation?
I think much of the perceived suddenness is that these types of pseudo-sexual or straight sexual fantasies don’t get talked about much between people in general and teenagers specifically are going to be less inclined to share that with even their friend if they think it might make them ‘weird.’ They might not even know they’re into it in the first place until they read the book. Look at 50 shades of grey for example. It actually started as a twilight fanfic then became the fastest selling series ever. Most professional reviews of the book are quite negative so why did it sell so well? It sold a fantasy. Something western society says you shouldn’t talk about because it’s inappropriate but no one can stop you thinking about it or liking it. Twilight also sold a fantasy but to a very large demographic. Then once people saw the monetary value in it they made big budget movies and all the attention made it a cultural movement and once you get to that point it’s a part of history, no one can go and erase it all. Plus young women will always exist and in western society twilight is this fantasy that they can enjoy so even if it might not be as prevalent wait once was twilight will always have some sort of audience.