Perhaps there is a family - related magical ailment that has been passed down. Since his parents were involved in the wizarding war, they could have been exposed to some dark magic that affected their genes in a way that is now causing Harry to be sick at such a young age. Or it could be something as simple as a magical virus that young wizards are more susceptible to.
It could be due to neglect. If we consider the situation in the Dursleys' household, they might not be taking proper care of him. They could be depriving him of proper nutrition or warmth, which could lead to him getting sick easily. Also, he might have been exposed to some dark magic residue in the environment that is affecting his health.
One possible reason could be a magical curse placed on him. Maybe some dark wizard who hated his parents decided to target him from a very young age. Another reason might be related to his unique magical nature. Since he is so powerful, his magic might be unstable at such a young age and could be making him sick as his body tries to adjust.
In a Naruto sick fanfic, one possible reason for his illness could be a curse. Maybe he was targeted by an enemy ninja who cast a powerful and slow - acting curse on him. This curse could be sapping his chakra and making him physically weak.
One possible reason could be a magical curse. In the world of Merlin, there are many dark sorcerers who might target Arthur. Another reason could be a poisoned weapon. If he was injured during a battle, the poison on the blade could make him sick. Also, it might be a result of some ancient plague that has resurfaced in Camelot.
Sirius, if he were aware of Harry's situation, would be extremely worried and desperate to get to Harry. He would feel responsible for protecting Harry, just like he felt towards James. He might even try to break any magical barriers or rules to get to Harry and take him to a safe place where he could be cured. And Hagrid would be heartbroken. He would bring little gifts like a small magical creature or some warm clothes to try to make Harry feel better.
Often, his illness is portrayed as something that makes him vulnerable. For example, he might be shown with a flushed face and a weak voice when he has a fever.
Mental health issues might be a factor. A 16 - year - old with undiagnosed depression or anger management problems could be more likely to commit violent acts. Also, being influenced by violent media or a bad group of friends can play a role.
One reason could be revenge. Bellatrix might want to get back at Harry for causing problems for Voldemort and the Death Eaters. Kissing him could be a form of humiliation. Another reason could be a power play. By kissing Harry, she shows that she can get close to him and has some sort of control over the situation.
One reason could be the strict control by the official copyright holders. They might be worried about fanfic diluting the official brand or misinterpreting the original story. Another factor could be some fans' purist view. They only want to stick to the original works by J.K. Rowling and consider fanfic as something not in line with the 'true' Harry Potter universe.
Maybe Dumbledore discovers some dark secret about Harry's past that he can't handle. It could also be that Dumbledore is trying to protect Harry in a really strange way, by pushing him away from the dangerous wizarding world around Hogwarts.
One reason could be to save him. Maybe Harry is injured during a battle or some sort of magical accident, and Snape, despite their differences, steps in to carry him to safety. For example, if Harry is hit by a dark curse and Snape, with his knowledge of dark magic, knows he needs to get Harry to the infirmary quickly.
Perhaps the author is trying to be different. Since so many fanfics already focus on Harry and Quidditch, they choose not to.