Eventually, Percy could become more determined. After the initial shock and anger, he would realize that he needs to be strong. He might use his mother's departure as motivation to become a better demigod. He could focus on honing his skills, making new alliances, and preparing for whatever challenges lie ahead, all while still hoping to get his mother back.
Percy might be very confused at first. He would wonder why his mother, who has always been there for him, suddenly left. He could start to question if he did something wrong. In some fanfics, he may go into a state of denial, not wanting to believe that she's really gone.