It could be an old enemy like Luke. He has always had a vendetta against Percy and would not hesitate to cause him harm. Maybe Luke has some new evil plan and hurting Percy is part of it.
In the hunt fanfiction, Percy might be hurt physically. For example, he could get injured during a hunt gone wrong, like being attacked by a wild beast or getting caught in a hunter's trap.
Maybe in some fanfictions, Annabeth could be written as betraying Percy's trust. For example, she might side with his enemies or reveal his secrets, which would deeply wound Percy emotionally.
Well, it could be that Percy gets physically injured during a battle. Maybe he's fighting some mythical creatures and one of them manages to land a serious blow on him. His friends then have to figure out how to heal him while also protecting him from further harm.
In many Percy Jackson fanfictions where he gets hurt, it often leads to his friends rallying around him. For example, Annabeth might use her wisdom to find a way to heal him quickly. His demigod powers could also play a role in his recovery, like his connection to water might help soothe his wounds if they're burns or something related to fire. It's a common trope to show his vulnerability and the strength of the bonds he has with others in these situations.
In some fanfictions, Percy's sister might hurt him emotionally by betraying his trust. For example, she could share his secrets with others, making him feel exposed and betrayed.
In certain fanfictions, Poseidon might hurt Percy's reputation. He could do something that makes the other demigods look at Percy in a different, negative light. This could be by making decisions that seem to favor Percy too much, causing jealousy among others, or by getting Percy involved in some political mess within the godly realm that Percy has no control over. This can lead to Percy being ostracized or having to deal with a lot of unnecessary drama and pain.
Another theme is isolation. Sometimes, when Percy is hurt, he may isolate himself from his friends, thinking he's a burden or that he needs to deal with his pain alone. This theme often leads to his friends having to break through his barriers and show him that he's not alone, which is a really heartwarming aspect of many 'Percy Jackson Hurt Fanfiction' stories.
One common theme is redemption. Since Percy has often made mistakes in the original story, in these fanfictions he usually tries to make up for his actions while dealing with the pain of his past. Another theme is family. His estrangement from his family causes him a great deal of hurt, and fanfictions often explore how he tries to reconcile with them.
Percy's performance in future hunts could be affected. Mentally hurt, he may make more mistakes due to lack of confidence or focus. Physically hurt, his skills may decline until he fully recovers. His overall attitude towards the hunt could also turn negative, which would not only impact him but also those around him in the hunt fanfiction.