Perhaps James had some hidden magical ability that he was unaware of until that moment. It could be something that was passed down through his family but had never manifested before. This ability could have protected him from Voldemort's killing curse. Or, it's possible that there was a plot by some other characters to save James. There could have been a group of wizards or witches who had been secretly working to keep James alive because they knew his importance in the fight against Voldemort. They might have used some sort of time - turning magic or a protective charm that Voldemort couldn't break through.
One reason could be for the sake of novelty. Fanfic writers like to create unique and unexpected scenarios, and this is a very different take on the Potter family. It grabs readers' attention.
One possible reason could be a dark magic influence on James Potter in the fanfiction. Maybe he's been cursed or possessed, causing him to act out of character and disown Harry.
The threat to his friends. James is very loyal to his friends, like Sirius, Remus, and Peter. If they were in danger or if something bad happened to them, it would be understandable for him to cry. For example, if one of them got seriously injured or was in a life - threatening situation, his emotions would be on full display.
Some fans might create it as a form of shock value. They want to stand out by presenting a very different and controversial take on the relationship between James Potter and Harry.
One possible reason could be that he was poisoned. In the wizarding world, there are many dark spells and potions that could cause such a reaction. Another reason might be extreme motion sickness if he was on a wild magical ride, like on a particularly unruly broomstick or a flying magical creature.
One possible reason could be an alternate universe scenario. Maybe in that fanfic's universe, there are dark forces at play that make Lily and James act out of character and ignore Harry. It could also be a plot device to create a more angsty or dramatic story, where Harry has to face challenges without the support of his parents.
One reason could be the hero - centric nature. Just as James Bond is the central figure in his adventures, Harry Potter is the focus in his own story. They both embark on dangerous quests and have to outwit their enemies. Another reason might be the element of secrecy. Bond has his spy secrets, and in Harry Potter, there are many secrets within Hogwarts and about the wizarding world.
Well, a great James Potter survived fanfiction is 'James Potter's Redemption Arc'. It could explore how his survival changes his perspective on life and death. Maybe he has to deal with the guilt of leaving his family behind in the first place. Then there's 'The Return of James Potter'. This one might show his struggles to fit back into the wizarding world he once knew, as so much has changed since his supposed death.
If he failed to follow the rules of the Marauder's Map. Maybe he used it in a way that endangered himself or others. His family, who are well - aware of the power and potential misuse of the Map, would ground him to ensure he understands the importance of using magical items responsibly. In his grounded state, he could be exploring the history of the Map and learning from the mistakes of previous users.
One possibility could be that there was some sort of magical interference. Maybe a powerful magical artifact or a spell was in place that deflected the Killing Curse just enough for James to survive. For example, if there was a hidden protection charm on him that he wasn't aware of.