So this is kind of my rant on fic writers who break up Percabeth. I get wanting to have other pairings, and I'm not criticizing others for what they like. It's just the ones where Annabeth betrays Percy post HoO doesn't fly with me (like in Purgatory by BloodRedDemon, which is a great story btw).
This is basically how I'd have to set up Purgatory so that Annabeth's betrayal is deeper, and makes more sense, and how to erode Percabeth as a ship.
In PJO, Percy is obviously still in love with Annabeth, but she never really gets over Luke and keeps stringing Percy along. After TLO, she can't really forgive him for killing Luke, but gets together with him anyways (at least outwardly) since he's currently the most powerful demigod around, and she's an ambitious bitch (don't ask why Percy loves her so much, idk).
When he goes missing at the start of HoO, she only looks for him because he's the most powerful, but she does 'shop around'. When Jason shows up, Cameron is with him, and they sort of get together.
Percy's mindset his whole demigod career is 'how do I win with the least amount of effort?', not because he's lazy, but because he's been persecuted for his power, so he suppresses as much of himself as possible until absolutely necessary. In HoO, the gods need heavy hitters, so they all praise Cameron (who, while not as strong as Percy, seems to be way more powerful since he shows off). Cam goes out of his way to show off his powers in the best light, and he and Annabeth really get together incognito.
In SoN, Percy's still in love with Annabeth, and she's the only thing he remembers of before, and SoN basically goes as usual.
MoA reunion Cam and Annabeth are incognito since both agree that having Percy break down would rob them of a pawn. Cam and Annabeth start plotting to take Percy down after the war. The MoA scene where Annabeth gets dragged down is slightly different, think of that scene in LotR movie where the Balrog's whip grabs Gandalf. Arachne launches a web at Annabeth, and Percy intercepts, getting dragged down. Cameron 'tries to save him' and pulls a Scar to Percy's Mufasa.
Tartarus basically goes the same, without Annabeth, Percy gets dark real quick, and when confronted with Akhlys he strangles her with her own poison no hesitation. This is where you first see his ability to absorb immortal's domains/powers. He meets with Bob and Damasen, and they start to help him suppress the darkness (first start to see Purge appear). He's still in love with Annabeth, and manages to make it out and close the Doors of Death.
On the other side, basically everyone buys the whole 'Cam is so great' bit. Annabeth pretends to be with Percy while the war is on, and most stuff goes along with canon (except the lovey bits are one sided, and Annabeth always makes excuses to go bang Cameron).
After the final battle, everyone is celebrating, and Percy sees Annabeth sneak off to the Poseidon cabin (he doesn't know she is sneaking off to be with Cam and assumes she wants to finally get 'intimate'). He finds the two in his own bed and he storms off, giving the couple their opportunity to take him down.
They frame him for the attempted rape of a few minor goddesses and Cam disguises himself as Percy, with Annabeth to provide him with an alibi. When Artemis finally catches him, she sees the betrayal in his eyes, but she has to take him to Olympus. In front of the Council, Cam and Annabeth lay out their 'evidence' and Percy gets cast into Tartarus.
That's pretty much it. IMO, canon Percabeth post HoO is too strong to break up with a betrayal from either party (there were a couple I've read where Annabeth saves Percy by intercepting Zeus' master bolt when they fear his powers, and that kind of break up I buy). You have to erode the foundations to make a betrayal work.
Hope I don't come off as a jerk for critiquing other's writing, but there it is. Idk if I'll write this out properly, probably not, since I love Percabeth too much, but feel free to take my ideas and run with them.