Do you have anymore of this written? Annabeth's way of helping Percy actually making it worse until he runs away and finally gets a taste of peace elsewhere? I love it so much.
https://www.tumblr.com/happyk44/749307578218053632?source=share
Pretty sure I've written something (or a couple somethings) similar to that piece before. It's a concept I really like. One of my first "Percy runs away to the Nome" pieces points out that Annabeth has been kind of preparing for the inherent trauma in being a demigod under the thumb of not so helpful gods her whole life compared to Percy who was thrown into it at random and retains a lot of bitterness over it versus passive acceptance the way Jason and Annabeth have kind of grown up to. Yeah, she has her beef with Hera but like. More or less, it's kind of "that's just how the gods are" with her and Percy is very much "well they should be fucking better".
I think that with her having known she was a demigod since she was a little kid, the difficulties she went through in getting to camp with Thalia, Grover and Luke, Thalia's sacrifice and seemingly having been holding onto the possibility of war at least since she was 12 and Percy came flailing into her life and into the prophecy - she's just able to compartmentalize her pains better than Percy who we know suffers more aptly with emotional regulation and anger issues. Whether she processes them in a healthy manner through this or represses, represses, represses is up to you, but I can see it being her default, and subsequently she gets very stressed out about Percy not being able to do the same thing.
Also people just process trauma differently and Annabeth gets very headstrong and stubborn about being right and that her way of doing things is superior (which is. like. one of the reasons I lowkey wanted to add her to the cluster B roster because imo her fatal flaw would fit NPD so well, but unfortunately I don't think enough of the diagnostic criteria suits her so RIP). So her way of handling trauma not working for Percy doesn't make sense to her, or the fact that Percy is still clearly having problems even if he pretends otherwise just makes her feel like he's not trying hard enough to get over it, so she starts pushing in ways that don't help because she's Annabeth and she knows how Percy works and she can map his way through this and if he would just try, then it would work (except they don't and they won't).
I've also mentioned before that Annabeth strikes me as someone who gets so beholden to her ideas and plans that any deviation from that plan (even if not well-thought out) is Not Allowed, and no matter how obvious the solution (change course, make other decisions, break-up and stay friends), she is extremely reluctant to do so. In Tartarus, she clung to the idea of her and Percy making it out alive and safe and moving to New Rome and being happy and going to college and growing old together and now, faced with the reality that the goal is likely unattainable (I really don't see Percy moving to California for college of all things, like let's be real) or facing some hitches (Percy's depression and self-isolation negates the whole happy and healthy thing), she gets further into her head about him not being able to get with the program.
So she tells him how to fix himself. He can't do it because her methods don't work for him like they work for her. She gets mad because there's no improvement from him and she doesn't know what else to try because she's exahusted all the options that Make Sense and Will Help Him and her way of doing things is right so he must be doing something wrong or not trying at all. He starts to withdraw from her because Percy doesn't really instigate fights and he's angry and unhealthy and doesn't want to hurt his girlfriend, and she gets mad because that's not how this is supposed to work, and they argue and the cycle just continues over and over and over again unti he's gone.
Personally I can write Percy disappearing in a bunch of ways. He fakes it until he realizes he can't make it and no one notices. He fakes it and people notice but they can't get him to open up about it. He suffers obviously but no one knows how to help him and he refuses to communicate. It will always culimaniate in him turning to isolation, turning to self-harm, turning to suicide, turning to whispering Carter's name like a desperate lifeline because if he kills himself Grover might die and his mom might be sad (he doesn't know, Estelle is there and she's good and she's normal and it's fine, his mom doesn't really need him, does she?) and Annabeth would probably be mad at him.
And if he calls out for Carter and he doesn't come or he doesn't care, well, then at least he can say he tried getting help, right? He didn't give up right away. He tried.
(Carter will always come and always offer the Nome as sanctuary and Percy will always accept it, even if he freaks the fuck out when they get there)