TL;DR: Based on the genetic progression we have observed in ourselves and other species thus far, at least 300,000 years and possibly more than 700,000 years of strict genetic segregation would be required for humans to see an irreconcilable genetic difference between genetically-segregated humans, heralding the creation of a truly distinct species of humans. The only way such a genetic divide could have developed during a period of maybe a millenia or two of feudal rule is for some more acute reproductive change to have occurred within one population or the other.
Speciation, the process of one species becoming genetically distinct from its parent and from any "sister species", thus unable to freely interbreed, takes quite a while. The most recently-diverged genii we are aware of are Ursus ("true" bears including black, brown and polar), Canus (dogs, wolves and coyotes), Vulpes (foxes), Panthera (large cats) and Felis (small cats) genii. All of these show evidence of easy hybridization among species within the genus, but they cannot freely interbreed to produce viable offspring in all combinations of mother and father and so they are indeed separate species.
Which is the first problem with your posit; even if humans do diverge genetically across social strata, it's very likely that viable offspring will still be possible in at least one combination of species and sex for many millenia after that, much as we see among relatively closely-related genii. Those hybrids, whichever society they mingle with, will infuse their genetic material gained from the other group through several generations of their descendants, which will help perpetuate the close genetic relationship between species and, if these trysts are common enough, even prompt a re-merging of the species by introducing enough of what makes one population genetically incompatible into the DNA of the other population, until some critical mass is reached that allows free interbreeding again.
The second problem is that even the most recently diverged genus, Canus, split into its extant sister species between 50,000 and 115,000 years ago. That represents about half that many generations depending on specific species and behavior, with female wolves sexually mature in a year, but not commonly leaving their birth pack until about 2-3 years of age as they're courted by unrelated males to become alphas. Extrapolating that 25,000-generation minimum to humans, with a roughly 20-year maturation period to a more socially-defined marriageable age, we'd expect even the weakest degree of speciation, losing at least one combination of parentage to nonviability, to occur over a span no shorter than 500,000 years of strict separation of the genetic stock, giving the genetic webs 25,000 generations of separation from any common ancestor. Even using the onset of female puberty (about 12 years of age) as the age of maturity and thus the minimum span between genetic generations, we're still talking about 300,000 years of genetic separation.
Now, that's a minimum timeframe. It also represents about the sum total of Homo sapiens' existence on this planet. We know that before Neanderthal man was out-competed by anatomically modern humans spreading from the Mesopotamian region about 50,000 years ago, Neanderthals and modern humans intermingled, with every non-African population of humans retaining about 2.8% of the Neanderthal genome. That genetic mix represents a confluence of DNA previously separated by as much as 700,000 years, when the genetic branch that resulted in Neanderthals first split from our own about 860kya. Whether all combinations of Neanderthal and modern human, male and female, produced viable offspring (and therefore H. neanderthalensis and H. sapiens were still genetically the same species) is unknown, but it's unlikely, given the proliferation of Neanderthal DNA in the human genome, that this was a rare occurrence.
So, while 25,000 generations is a minimum timeframe, giving us a neighborhood of between 300k and 500k years to start seeing genetic speciation happen in genetically-segregated humans, we also have archaeological evidence that anatomically modern humans didn't truly segregate from Neanderthal cousins over a timeframe up to twice that long. At the upper end of canine speciation estimates and human maturities, we might expect genetically-segregated humans to truly speciate on a timescale of a million years (but still produce viable hybrids from the male of one species and the female of the other). In any case, expecting it to happen naturally as the result of even a couple millenia of social segregation between cohabiting human populations just doesn't pass the smell test.
So, the only feasible scenario for your worldbuilding is that some more acute genetic mutation has rendered the nobility incapable of producing viable offspring with the rest of humanity. This mutation could be environmental in nature, or could arise quite simply by inbreeding among a small genetic population.
The first device is a fairly easy handwave and it's been done before. In the video game Freelancer, the Outcasts are the descendants of one tribe of the doomed sleeper ship Hispania, and landed on a planet with a predominant form of plantlife that ended up altering the Outcasts at a genetic level, making them unable to tolerate being away from the Outcast homeworld Malta for any extended period without a supply of an extract of the plant, called cardamine.
In another example, the Divergent Series novels and movies ultimately reveal Triss's home city of Chicago to be an experiment by a far more advanced branch of humanity that survived a global war. Chicago's inhabitants were genetically damaged by weapons used in that war, limiting their inherent human traits, and the experiment, run by the descendants of humanity who escaped such weapons, sought to find out whether the genetic damage would naturally heal over time. Divergents, ostracised and hunted down as undesirable by Chicago's leadership (totally unaware of the experiment), turn out to be exactly what the experiment was intended to produce, as individuals' genomes repaired themselves over generations. Reproductive difficulties weren't covered specifically, but this is an obvious direction to take an underlying story about a society of genetically-damaged individuals.
The second device, simple inbreeding, has pretty sound basis in our own reality. Estimates of the "minimum viable population" of a genetically random or localized population hover around 4,000 individuals; any fewer than that and you will, given sufficient time, see symptoms of inbreeding caused by insufficient genetic diversity. You can make do with a smaller population if that population is more genetically diverse, down to a minimum hypothetical "ark population" of approximately 500 individuals, specifically selected from across the entire human species to maximize diversity across the genome, and then the proper sequence of reproductive pairings "arranged" through each generation, stud-book style, to disseminate that genetic diversity as efficiently as possible.
As of the creation of Great Britain in 1707 by the formal merging of the crowns of England and Scotland (which had rested on the same head since James VI of Scotland inherited the English crown from his cousin Elizabeth I in 1603 to become "James VI and I"), the "peerage" or nobility of both predecessor nations numbered only 322 individuals and their extended families. Let's say the average family size, including only children surviving to have their own children, was 5; that's only 1500 individuals in a roughly steady-state population, many of which could likely already trace their familial relationship to most of the rest of the peerage within four degrees of blood or marriage on both sides of their family tree, well below the 4,000 minimum viability of a random localized genetic sampling.
It's a long-running joke that the English nobility have kept it in the family just a few generations too many, and while both the sons of Charles and Diana have married and had children outside the nobility, Prince George (William and Kate's eldest son) is the first person in line to the British throne that I can find since the Tudor era (Edward VI, son of Jane Seymour) to not have two parents of noble birth.