In some fanfictions, Percy could lose hope because of the gods' indifference or harsh treatment. He has always been in a complex relationship with the Olympians. If they were to unjustly punish him or his friends, or turn a blind eye to the real problems in the demigod world, Percy might feel like all his efforts are in vain and lose hope as a result.
One possible storyline could be Percy losing hope after a major betrayal by a close friend in the demigod world. Maybe he feels like he can't trust anyone anymore and starts to isolate himself from his usual group. This could lead to a downward spiral where he even questions his own abilities and purpose.
One possible storyline could be that Harry faces a series of seemingly unbeatable dark wizards. He has lost so many friends in the battles and feels like no matter what he does, more harm comes. Another could be that he fails an important mission to save Hogwarts and the guilt makes him lose hope. He might start to isolate himself from the wizarding community.
One possible storyline could be Percy leading a Titan rebellion against the Olympians. Since he has a connection to the Olympian side as well, it would create a very interesting internal conflict for him.
One possible storyline could be Percy forming a band with his demigod friends. They could go on a tour across different mythical realms, performing for gods and monsters alike.
Perhaps Percy is a single dad because his partner was lost in a battle against the Titans or some other great evil. In the fanfiction, he could be dealing with the grief of that loss while still being a great father. He might take his child on adventures around the places he used to go as a teen demigod, like the Labyrinth, but this time it's to teach his child about their heritage and how to survive in a world full of mythological threats.
One possible storyline could be the OC being a new demigod who catches the attention of both Percy and Artemis. Maybe the OC has a special power that is crucial in a new threat that's emerging in the world of the gods. For example, the OC could have the power to control time briefly, which becomes important when an ancient enemy tries to rewrite history to gain power.
One possible storyline could be that they discover their sibling relationship while on a quest together and have to deal with the shock and how it changes their view of each other.
The main antagonist could also be a new and unknown force from the Underworld. It could be a powerful spirit or entity that is spreading despair among the demigods. Percy tries to fight against it but finds it so difficult that he begins to lose hope in the face of this seemingly invincible foe.
In a fanfiction, Percy could lose an eye while on a quest. Perhaps he's exploring an ancient, cursed temple. There are hidden traps everywhere, and as he's trying to solve a riddle to progress, one of the booby traps activates. A sharp blade swings out and hits his eye. This event could change his relationships. Some friends might be overly protective, while others might not know how to act around him. Percy would then have to prove that he's still the same hero, just with a new challenge to overcome.
One possible storyline could be Percy trying to hide his panic attack from his friends at school because he doesn't want them to worry. He might run off to a secluded spot like an old janitor's closet to deal with it on his own. Another could be that a new monster shows up at school disguised as a student or teacher, and Percy's panic attack is triggered by his sensing of the monster but not being sure where it is. Or perhaps Percy has a premonition of a future danger during a class, which causes the panic attack and he then has to figure out how to prevent what he saw from happening.
One possible storyline could be the challenges Thalia faces while pregnant in a world full of mythological threats. She might have to rely on her friends more than ever. For example, Percy could be there to protect her from monsters that target her because of her condition. Another could be the emotional turmoil she goes through, as being pregnant might change her role in the group and her own self - perception. She could struggle with how this new situation affects her goals and dreams within the context of the Percy Jackson universe.