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.
A new, powerful monster could be responsible. For example, a monster that is specifically designed to target Percy because of his status as a powerful demigod. This monster might have some unique abilities that make it difficult for Percy to defend himself and thus gets hurt.
It could be an enemy that manages to sneak onto the Argo 2. Maybe a monster that they thought they had defeated before but actually just bided its time and then attacked Percy when he was least expecting it.
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.
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.
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.
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.
Another possibility is a jealous student at Hogwarts. There are always students who might be envious of Hermione's academic achievements. They could set up a prank or a trap that goes wrong and ends up hurting her. For example, a student who is tired of Hermione always getting the top grades in Potions might tamper with her cauldron during a class experiment, resulting in an explosion that hurts her.
Perhaps it's part of a grand plan that Poseidon has, one that he believes will ultimately benefit Percy but in the short - term causes him pain. For example, he might be trying to toughen Percy up or make him prove himself in a more extreme way, thinking it will help Percy in the long run.
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.