They once were a prestigious family or society known for producing strong magic users, but over the years something changed and now those born are weaker, if they're lucky, and unable to use magic at all if they're unlucky.
Very often no one knows exactly why this has happened, and how those affected choose to respond may actually make it worse, such as using inbreeding to try and preserve desired traits, but this rarely works as more than a stopgap and usually just causes other problems. Many try to keep this a secret once it's discovered in an attempt to hold on to their status.
If a child is born and turns out to be as strong as previous generations or even stronger they're likely to be a protagonist or have great importance in the story, and may be The Chosen One.
- The mononoke race in Mononoke Sharing has become progressively more human over the generations due to them not having been part of the plan of the gods when the world was created, which is why they all appear as Cute Monster Girls. It's mentioned near the end of the series that all of them will be born fully human within the next few decades.
- In Runaways, Nico's family has dabbled in magic for centuries, but according to her ancestor, the Witchbreaker, the magical talent was already beginning to diminish sometime during her own era (the 1900s), and she herself is a hostage of the Upward Path, and thus she decides to subject Nico to Training from Hell in the hopes of keeping the family business alive.
- In Wish Carefully, the result of the Dark Wizards of Voldemort's regime being cut off from the Light side of the world means they've had centuries of inbreeding, which has gradually produced fewer and fewer magically-capable children every generation. In the one Lucius is writing about in the fic, only four such children were born, and they're so weak that they can't even pass the sixth-year courses at Hogwarts because they don't have enough power.
- Discussed in Harry Potter and the Methods of Rationality — this is the claim being made by the Death Eaters, and more precisely, that it's because wizards are allowing muggle blood to dilute the power of magic. Harry notes that it's a persuasive story: from Muggle history books, he's well aware of the standard fascist narrative of "society was once great but is now crumbling, and it's the Hated Other's fault" and just how well it dupes the unwary — and he knows how to counter it, too.
- In A Discovery of Witches witches and wizards are becoming less powerful, daemons are becoming more unstable, and vampires are finding it more difficult to create new ones. Diana and Matthew's children, the "Bright Born", half-witch, half-vampire create a new race that will revitalize magical creatures.
- The Targaryen family in A Song of Ice and Fire carried out generations of BrotherSister Incest to preserve their Valyrian looks, connection to dragons and the apparent magical powers that likely kept them from being even more deformed because of the repeated incest, but by the time of the main series no one has been able to successfully hatch a dragon for several generations. Until Daenerys comes along and not only hatches three but proves she has the legendary resistance to fire near the end of the first book. Additionally she's one of the most likely candidates for the Azor Ahai, who will defeat The Others.
- In the Harry Potter series, a desire to prevent this is a major motivation for blood purity fanatics, who insist on marrying only other pureblooded wizards with no muggles in their family trees out of a belief that intermarrying with them will weaken their family lines. Yet the only case of this actually happening that we know of occurred within the Gaunt family, a family of purebloods who were so inbred that they were prone to insanity, mental instability and reduced magical ability to the point that Merope Gaunt was believed by her father to be a Squibnote . And just to prove how false the whole fear about intermarrying with muggles was, the strongest member in generations, Tom Marvolo Riddle, aka Lord Voldemort, had a muggle father.
- Interestingly, many of the Squibs we know of are half-blood, according to Word of God revealed on Pottermore: Lockhart is a half-blood and his two sisters are Squibs, as is Dolores Umbridge's brother, and Isolt Sayre, Slytherin's descendant who founded Ilvermorny had two daughters, a witch, and a Squib. Yet at the same time several notably skilled and powerful wizards like Albus Dumbledore and Serverus Snape are also half-blood, making the diagnosis of the concept difficult to determine.
- In Miss Peregrine's Home for Peculiar Children, it is believed by some that the peculiars of the story are descended from a handful of peculiars who were extremely powerful, and the size of giants. As they multiplied, their powers diluted, and as they became less powerful they shrank.
- A plot point in Mistborn: The Original Trilogy is that fewer and fewer Allomancers are born into the nobility, and those that are aren't as powerful as they were when the Lord Ruler first created the Mistborn. Mistborn are rarer among Allomancers, as well. By the time of the sequel series, Wax and Wayne, Mistborn are regarded as half-mythical, and even "full" Feruchemists seem to have disappeared, with only single-power "mistings" and "ferrings" remaining. But interbreeding between Terrismen and others have lead to Twinborn, those with one Allomantic and one Feruchemical power. Word of God is that by Wax and Wayne, Allomancy has gotten as weak as it ever will, so the decline will not continue into later books.
- In The Wheel of Time, this has been happening throughout the main continent as a result of the magical establishment systematically hunting down males with magical ability, which is necessary due to a taint on the male half of the Source, which causes all male channelers to inevitably go mad. The female establishment is aware of this problem, and partway through the series starts to consider some fairly severe policies in the hope of stopping the decline. Ultimately, the problem is solved when the taint is removed, allowing males to live without overt persecution.
- Stargate Atlantis: The Atlantis expedition encounters one culture whose royal family have used Ancient technology to protect their people from the Wraith because they are the only ones who possess the ATA gene that is required to operate it; a problem the main characters also had when they started using Ancient tech before finding a way to inject everyone with an artificial ATA gene. Despite efforts to strengthen the bloodline through careful breeding, their control is clearly diminishing. Sheppard is propositioned by the female heir to the throne specifically because his strong ATA gene will strengthen her child's claim over that of her brother's.
- This has happened to humanity as a whole when it comes to magic, with modern Magi only a shadow of what they used to be in The Time of Myths, which explains part of why the Servant characters capable of using magic in the Fate series are so much stronger than the modern humans. The goal of Magi in general is to try and recapture the True Magic that their ancestors had a much easier time accessing. The individual games also have specific examples of this:
- The Matou/Makiri family from Fate/stay night was once one of the preeminent families in the Mage's Association and one of the three families who started the Holy Grail War, but ever since leaving their homeland of Russia and settling in Fuyuki they've been growing gradually weaker until their latest heir, Shinji, has no magic circuits at all, necessitating the adoption of Sakura Tohsaka into the family so the family could still participate in the War, something Shinji heavily resents her for. No one's entirely sure why this has happened but the Matous claim it has something to do with Fuyuki's energy being incompatible with theirs. There's a vague implication it might be related to family patriarch Zouken and his methods of staying alive.
- In Fate/strange fake, False Archer's unnamed original summoner mentions many magical families have been getting weaker with each generation, including his own. He tried researching ways to prevent this in his son, but when his son turned out to have less potential than himself, he killed him, then his wife for trying to stop him and for failing to provide him a strong heir. He was planning to win the Holy Grail War to wish for greater power and for strong heirs, only to be quickly murdered.
- The Nanaya family in Tsukihime used inbreeding to try and prevent this due to their power as an "anything killer" and served the Demon Hunting Organization for generations until they were slaughtered prior to the start of the story.
- Kara no Kyoukai:
- The Asakami Clan of the Demon Hunters Organization was a clan of powerful telekinetics, but had been undergoing decline as a result of too much interbreeding, with the main house eventually dying out and only minor branches remaining. Fujino Asagami was the strongest member in generations but had her powers sealed as a child, only to have them come roaring back at an inopportune time.
- The Aozaki clan was undergoing this prior to the birth of Touko, who was born with an astounding number of magic circuits considering her parents had none. Later on, in Mahou Tsukai no Yoru her sister Aoko proved to be a prodigy capable of using the True Magic even though her number of circuits was average at best. When Aoko was chosen to be the family head over her sister the fallout was enormous.
- The Yayoi clan in BlazBlue was one of the 12 families that formed NOL and were extremely powerful, but they panicked when they started producing children with weaker Ars Magus abilities and started marrying within the family in the belief it would make them stronger. The other members of NOL are noted to be disgusted by this, with the head of the organization even telling them to stop. Things have gotten so bad that Tsubaki is specifically noted to not be the first child of her parents, simply the first to survive early childhood.
- Wyndia's Wing Clan from Breath of Fire have the ability to transform into giant birds at free will and all have wings with which they can fly. This ability is dying down as time passes, only choosing the select few, and will eventually disappear altogether. This was revealed in Breath of Fire II. Nina from the first game was to blame for falling in love to a man from another clan and weakening the power.
- In The Elder Scrolls series, this (along with elements of Our Ancestors Are Superheroes) is at the heart of Altmeri (High Elven) religious beliefs. To them, the creation of the mortal world was a cruel trick which forced their divine ancestors to experience mortal suffering and death. They believe that the other "lesser" races of Mer are the result of "degeneration" over the ages, with each generation being weaker than the last as they are one more removed from their divine Aedric/Ehlnofey ancestors. (And don't even get them started on the races of Men...) The Altmer actively try to breed themselves back into their ideal (including, according to some sources, the culling of undesirable progeny), to maintain a perceived level of "purity".
- Implied to have been happening to the Llyn Imperial Family in Blindsprings prior to their being overthrown. They were having trouble producing the next generation, and protagonist Tamaura was tellingly both a strong nexus of Orphic power and born out of wedlock. Since Orphic magic is In the Blood most of the noble Orphic families were also somewhat inbred.
- The nation of Astoria from Darc Sowers' Code Name: Hunter used to run mostly on magic, with wizards and sorcerors aplenty. When covert agents Max and Ruby visit the island nation, one Astorian mage mentions debating with the Queen that wizards and acolytes are in decline, a symptom of diminishing magic overall within the realm. Word of God states that a nation's magic level is tied to the well-being of its people, and Astoria is losing magic because of their insane oppression of non-mages while people from prosperous first-world countries like Britain positively radiate magic. Which Astoria's queen has noticed, though she doesn't know why.