It could be Annabeth. Maybe they had a huge fight over something important, like the future of their relationship or a difference in their values regarding their demigod duties. And this fight led to Annabeth leaving Percy, which broke his heart.
His father, Poseidon, might be the cause. Poseidon could make a decision that goes against Percy's wishes or beliefs. For example, Poseidon could force Percy into a marriage with someone he doesn't love for political reasons among the gods. This would surely break Percy's heart as it would mean his father doesn't respect his feelings.
Another possibility is that the Pokemon themselves could be the cause, in an unexpected way. For example, if one of Satoshi's Pokemon gets seriously ill and needs to be left in a far - away place for treatment. Satoshi decides to stay with the Pokemon, but Haruka has to continue her journey. This difficult decision could lead to heartbreak for both of them.
Gary could also be the one to cause Ash's heartbreak. Maybe Gary outshines Ash in a big Pokemon battle and then mocks him for it. This could make Ash feel like a failure and break his heart. Gary has always been a bit of a rival to Ash, so this kind of situation is plausible in fanfiction.
Another character could be Kakashi. Maybe he has to make a tough decision that goes against Fem Naruto's wishes. For example, not allowing her to go on a dangerous mission she really wants to. This could make Fem Naruto feel betrayed and heartbroken, as Kakashi is a respected figure in her life.
A new, powerful villain could be the cause. This villain might target Ash's Pokémon and manage to steal them all away. Ash would be heartbroken not only because he lost his Pokémon but also because he feels he has failed to protect them.
It could be his arch - enemy. For instance, the Joker might play a cruel trick on Nightwing that makes him lose someone he cares about deeply, thus causing his heartbreak.
A vengeful god could be the cause. For example, if Percy somehow angered Ares, Ares could manipulate the situation so that Percy gets arrested by mortals. He might use his influence to make it seem like Percy was involved in some sort of illegal fighting or destruction.
It could be a new, mischievous minor god or goddess. Maybe a god of miniatures who is jealous of Percy's fame and decides to shrink him as a prank. Another possibility is a rogue magician or sorcerer who has a vendetta against demigods and specifically targets Percy to make him less of a threat.
It could be a new villain. Maybe a villain who targets Naruto's loved ones and Naruto is unable to save them. This failure would cause him great heartbreak. For instance, if the villain kidnapped Hinata and Naruto couldn't rescue her in time.
One great 'Percy Jackson Heartbreak Fanfiction' is 'The Broken Hero' which delves deep into Percy's heartbreak after Annabeth's unexpected departure. It shows his struggle to come to terms with the loss and how it affects his daily life and his relationships with other demigods.
Perhaps he has a childhood friend, Tom, who also joined the army. Tom is more of a follower type, always looking up to Percy for guidance. And then there's a foreign - born soldier, Ahmed, who brings a different perspective and set of skills to the group. Ahmed might be really good at stealth operations and teaches Percy some new techniques.