Percy was just done.
It didn't matter to him anymore that his life seemed to be going well. His girlfriend was alive and not currently madder at him than usual. His friends were all happy and alive (at least, most of them.)
What did matter to him, however, was the fact his past was haunting him. No matter where he went, there would be some reminder of a failed attempt, a broken promise, a lost life. Leo and Calypso: although they were both happy, she was a failed attempt at justice. The scars on Annabeth's lower back and shoulder and arm and all over her precious, delicate body, received from protecting him and his failing to protect her. The couple he saw walking in Central Park who he could swear were Beckendorf and Silena. Every time he picked up a sword, all he could think of was when Chrysaor disarmed him. In front of ALL of his friends. He failed them, just like he failed so many other things. They needed him, and he wasn't able to help them.
He didn't know when he started becoming so unhappy. He hid it from his friends like he hid everything else; they couldn't know he was having trouble. It would burden them, and he could not do that to them. It wasn't fair to them, after all they'd been through. He could carry it for himself. They were his own burdens, after all.
He'd figured out a while back that he could suffocate underwater if he tried. He'd also done some exploring in the beach area of Camp Half Blood. Farther down, there was an area with rocks on the surface with a shallower depth. It was also near a bridge that lead to an island a select few knew about. This gave Percy the perfect opportunity to plan his own demise.
The day in question was a partly cloudy Thursday afternoon. There were some grey clouds on the horizon, but the ones above his head were white. Fluffy. Innocent. He had never thought of clouds as innocent before, but he thought it was a great thought. There wasn't enough innocence in the world, anyway. It was warm, too; the clouds occasionally passing the sun didn't prevent the heat from baring down on the earth of the camp. It was an appropriate day to go swimming. Nobody would think anything strange of it.
Percy sat at a desk in his cabin, pencil poised over paper, trying to think of words to say to each and every one of his loved ones. Words were definitely not his strong suit; neither were actions, he supposed. At least you can perfect words. You can never take back actions.
He figured short and sweet was the way to go. Annabeth, he wrote, you'd know what drove this better than anyone. My thoughts are too dark for you; I can't contaminate you any longer. You deserve better. I love you.
Mom, he continued, I'm glad you're happy. I am. I'm not, though. I don't think it's the type of unhappy you can fix, either. I love you more than anything, and hope you'll be okay.
His list continued on—he writes to Frank, Hazel, Leo, Piper, Jason, Thalia, Rachel, Nico, his dad, Reyna, anyone he could think of. He does not fail to write "I love you" in every note. He put his notes in one single envelope. On the front of the envelope, he quickly scrabbles: "I will be at the bridge- not alive. Check the waters." Although it breaks his heart to know he's hurting his friends, he can't continue to be haunted by all of his memories, his failures. That breaks his heart even more.
He heads out, towel over his shoulder and swim trunks on so nobody gets suspicious. He gives watery smiles to all he passes. When asked where he's going, he says the beach. When asked when he'll be back, he shrugs and says he doesn't know. What the asker doesn't know is that secretly, he's thinking, "Never."
After about 15 minutes of walking down the beach, the bridge rises in his vision. This is his chance to turn back; he does not take it. He steps onto the bridge as he gets there. On the edge, he sets the towel down. It's one of his mother's nice towels; he doesn't want anything to happen to it. He wants her to get it back, at least.
He jumps on the bridge, lets his feet dangle over the edge with his back to the way he came. He thinks about what led him to be sitting on this bridge. He's thinking about all the casualties because of him; his eyes begin to water. He thinks of all the promises he broke, intentionally or not. A single tear drops down his cheek. He thinks of the pain he's caused all his friends, because of his power and the power of his enemies. He thinks of the look on Annabeth's face as she begs him to stop controlling the poison in Tartarus. He starts crying, now; real, wet, drippy tears. He's been strong for so long, he doesn't know how to properly break down. He sniffles and bawls and coughs to the point he's spitting blood, not caring what state it puts him in.
Eventually, he decides to cut the self-pity. He came here for a reason, and he will accomplish his goal. He stands on the edge of the bridge, points himself towards the sharpest rocks. He's in the middle of his jumping stance when he hears a voice desperately call, "Percy! NO! STOP!"
The voice that has comforted him before startles him into jumping now. But a startled jump is different from a planned jump; you don't go far. Out of instinct, as he falls, he grabs onto the bridge railing as Annabeth, tears streaming down her cheeks like never before in her life, hair flying behind her like a fan was trying to kill her, comes running up to where he is on the bridge.
"Stop, please, Percy," she croaks, her voice quivering. "Come back up here. Please. I-I've already lost so much; I can't lose you too." He analyzes her face. He feels most guilty about leaving Annabeth; they'd been through everything together. She sees the resolve in his face, and she starts crying harder. "Percy, please! I can't-"
He cuts her off. "Annabeth, I just- I'm not cut out for this. I can't do this anymore." She takes a deep breath between the sobs racking her body. "We can help you, Percy! Just let us. Please. Let us be there for you like you've for us. Please."
It seemed the Fates had granted him his last wish; he could guarantee he had meaningful last words. He took a deep breath, pushed his arms up, gave Annabeth one last peck on her tear-covered lips. His words, almost a whisper, sounded painful; they were. It hurt him, too; it hurt him more than almost anything had hurt before. "I love you, Annabeth."
He dropped his arms back down, let go of the wooden railing, and plunged into the sea.
update: I have been asked if Percy can actually drown. I believe he can; the same way he can control if he gets wet and can get wet if he wants to, he can also control if he can drown or not. irony at its finest, I suppose, but I think if he wanted to enough he would be able to.