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Relegated Mentor
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Master: A cycle is complete, and now there is a new emptiness to be filled. A new journey, which you must take alone.
Bruce Leroy: Master, perhaps with more time to train. Master, I need more time.
Master: I am no longer your master!
— The Last Dragon
After training and teaching The Hero for years, the mentor becomes less needed and eventually leaves because, as he most likely will tell the hero, "you don't need me anymore." The mentor may say this with a proud sadness and The Hero more than likely will object to his teacher leaving, claiming that they don't have all the answers and that they will be lost and unguided without the help of the authority figure.
If the mentor is obsolete they will be relegated much more quickly, perhaps within a single episode. May overlap with Mentor Occupational Hazard, or the mentor may be Demoted to Extra in which case they are still in the series but mostly as an Out of Focus background character. Most cases, though, have the mentor being Put on a Bus.
In the Lyrical Nanoha franchise, Yuuno Scrya played a major role in the first season, mentoring the eponymous main character in the art of magic. However, he has been all but Put on the Bus by the third season, after Nanoha became a hypercompetent badass herself.
Master Roshi from Dragon Ball series wins the first tournament in the shows run, loses in the final 4 during the second, and doesn't even compete in the third. By the time Dragon Ball Z starts, he has become a minor character who isn't nearly as strong as the characters he previously trained. In fact, if you watch Dragon Ball Z before Dragon Ball, you could be forgiven for not knowing that he was ever the world's number one martial artist.
Inverted in most adaptions of Batman (and less so with Superman) seeing as he is the main character, his sidekicks leave him once they gain enough experience and become their own heroes, i.e.: Robin becoming Nightwing and Barbara Gordon becoming Oracle.
In Legion of Super-Heroes, Marla Latham served as the incipient team's Adult Advisor, helping to train and counsel the young group of teenagers. As the years passed, he came to feel that he was acting as an emotional crutch and holding back their development, ultimately retiring.
Wonder Woman (1987): Artemis acts as Cassie's mentor after Diana requests she look after her, but leaves shortly after Diana's return even though Diana does not really act like Cassie's mentor since Cassie seems to have the hero thing down.
Professor X from X-Men. Once his X-Men gain enough experience, they tend to leave and become part of other comic titles where they take a more central focus. Scott "Cyclops" Summers exemplifies this best when he takes over for Xavier as the team lead.
Fan Works
In Things We Don't Tell Humans, the previous Prime and Lord Protector are supposed to mentor and advise their successors until they are no longer needed. Terratron accepts this with grace, dignity, and a bit of enthusiasm. Sentinel Prime does not.
In Uzumasa Limelight, Seiichi's continuing loss of motor control and Satsuki's success as an actress lead him to quietly retire from acting completely, as he's less able to teach and Satsuki has little left to learn. Satsuki eventually persuades him to return for one last role as equals rather than mentor-and-student.
Happens frequently to Harry Potter in his series. All his mentors die, Dumbledore, Sirius, Lupin, leaving him alone and feeling lost. Dumbledore plays this the straightest though in that he willingly died and spent his last year preparing Harry to understand and defeat Voldemort.
This happens to Alaric Morgan relative to Kelson Haldane in the Deryni works. Morgan has a bigger role in the events of the Chronicles of the Deryni trilogy, but Kelson comes more to the fore in the next trilogy (called The Histories of King Kelson). It's justified in that Kelson is introduced as a boy of fourteen at the start of the Chronicles, and that entire trilogy takes place within the following year, so he lacks age and experience. The Histories take place a few years later, after Kelson has grown a bit and been on the throne for a while, and the third volume centers around Kelson's knightly accolade and the coming of age that represents. Morgan is still alive and well as a friend and advisor (the Codex lists him as such several years after the events of King Kelson's Bride), but his presence isn't as large as in the earlier works.
One of the protagonists of In Conquest Born, Anzha, is able to overcome a legal prohibition against her joining the military because Torzha, the head of the whole military acknowledges her potential and offers to sponsor her. Torzha's support makes Anzha's military career possible, but the extent of her effort on Anzha's behalf is opening doors. Eventually, political demands make Torhza less of an enabler and more of an impediment to Anzha.
Live Action Television
Leo does this to the girls in Charmed in an episode where he becomes and Elder and can no longer be around to personally give the sisters advice and inspiration. They spend quite a bit of time whining about how they don't know what to do without Leo there to guide them and give them answers. Leo informs them that they don't actually need him and are more than capable to solve their magical problem of the day without his help.
Giles in Buffy the Vampire Slayer left the Buffy and the Scoobies because Buffy had grown to be a capable leader without his presence.
Rebuilt Pedestal
Mentor Index
Renowned Selective Mentor
Now That's Using Your Teeth!
QuoteSource/Live-Action Films