There have been many losses on Game of Thrones, and one of the most recent deaths on the show is an especially hard hit for the Stark family. Rickon, the youngest of the wolf-sigil brood, was killed in Episode 9, "The Battle of the Bastards," in a truly heartbreaking way. But fans might not want to start mourning just yet, because with people like Jon Snow rising from the grave, we all know that dead doesn't really mean dead on this show, right? Rickon could come back to life, theoretically, but that's not to say it will definitely happen. After all, Jon ordered his body buried in the Stark crypt next to their father Ned, and if Jon and Sansa both knew that it was possible for someone like Melisandre to bring Rickon back to life, why didn't they ask her to do so? The answer might be because Jon doesn't think coming back from the dead is all that it's cracked up to be.
With Robb Stark dead, Bran becoming the three-eyed raven, and Jon still a bastard, the title of Lord of Winterfell fell on young Rickon Stark, whom fans hadn't seen since Season 4 when he was still a young boy. Viewers knew Rickon was in trouble the minute he appeared in Season 6, betrayed by Smalljon Umber, who captured Rickon and Osha and turned the child over to Ramsay Bolton. When Sansa and Jon learned that Rickon had been captured, they had different reactions. Sansa resigned herself to losing her brother. She knew Ramsay as a heartless torturer, and that he would use Rickon as bait in a sick game. She tried to convince Jon of this, but he still tried his damnedest to save Rickon's life. But in the end, Rickon was struck and killed by Ramsay's arrow.
But once the violent battle was over, why didn't Jon or Sansa immediately take Rickon's body to Melisandre so that she could work her magic and restore Rickon's life? His injuries didn't seem any more intense than Jon's multiple stabbings, and as the last male heir of Winterfell (assuming at this point that Bran is going to become a magical tree person of some sort rather than return home), Rickon was the only surviving male that could claim the title of Warden of the North. But Jon knew something of being dead, and he didn't necessarily like that he was brought back to life, so he might not have wanted that for his brother. Jon was clearly traumatized by the fact that he had been dead and saw nothing nor heard nothing in any kind of afterlife, and as he told Melisandre, he was pretty certain that he didn't want to experience that feeling again.
Jon: "If I fall, don't bring me back."Melisandre: "I'll have to try."Jon: "I'm ordering you not to bring me back."Melisandre: "I am not your servant, Jon Snow."Jon: "You're in my camp. I'm the commander."Melisandre: "I serve the Lord of Light. I do what he commands...If the Lord didn't want me to bring you back, how did I bring you back? I have no power. Only what he gives me and he gave me you."
Jon probably doesn't want to inflict the same trauma he experienced on his younger half-brother. Jon also may be aware that the resurrection process sort of "disintegrates" a person every time it's done. As Beric Dondarrion said, each time he's been resurrected by Thoros of Myr (and we're up to six at this point), "Every time I come back, I'm a bit less. Pieces of you get chipped away." In the books, Beric also says that he loses a huge number of his memories each time, and that he would never wish his life upon anyone. And book readers know all about Lady Stoneheart, and the half-human that she's become as a result of her resurrection. It's possible that Jon already feels what Beric is talking about, that a piece of him is gone, that he's just not the same, and that he may be slipping away from himself. There's no reason he'd wish that experience on innocent Rickon, just to provide Winterfell with an heir. And the fact that Rickon is still so young might have an even greater effect on his memories, personality, and sense of self.
That said, that doesn't mean Melisandre won't give it a try. As she told Jon, she doesn't have the power, it's the Lord of Light that does, and her only option, really, is to try to work her magic and see if that's what the Lord wants. But bringing Rickon back to life wouldn't be that great of a choice for the series, in my opinion. The show already has a problem with its death fake-outs, so bringing another character back would get repetitious. And, let's be honest: while Rickon was an important member of the Stark family, he wasn't necessarily an important member of the series. Losing Starks and other good guys is a bummer, because, after all, most of us want the Starks to win, but with the ever-growing number of characters on Thrones, fans can't deeply care about ever single storyline and family member. Plus, Rickon's death could mean big things for the show; with Bran off being a forest wizard and Jon still a bastard, this leaves the gate open for Sansa to become the Wardeness of Winterfell, which would be totally awesome.
So Rickon, sorry buddy. We'll miss you, but you're better off staying dead.