how does a reasonably large geographical area (at least a moderate country, preferably larger) sustain regular and drastic shifts in power (the more rapid the better) over a long period of time (at least living memory)?
The never ending war scenario you are describing is best exemplified by Afghanistan which has been embroiled in wars more or less continuously since the 1970s, leaving it the least developed country outside of sub-Saharan Africa in the real world. Initially, this was a part of the Cold War with fighters on the respective sides supported by the Soviet Union and the United States. When the Cold War waned, Saudi Arabian elites funded a new wave of proxy wars using this as a place to test run their Islamist political ideas via the Taliban against opium cartel fueled warlords loosely aligned with the "decadent" West.
The nearby example of Kashmir is another example of a sustained proxy conflict.
Another similar example is the Hundred Years' War "waged between the House of Plantagenet and its cadet House of Lancaster, rulers of the Kingdom of England, and the House of Valois over the right to rule the Kingdom of France. It was one of the most notable conflicts of the Middle Ages, in which five generations of kings from two rival dynasties fought for the throne of the largest kingdom in Western Europe." It was the primary model for the fictional Game of Thrones series of books and television adaptations of the books.
A third example would be the Islamic empire's seizure of Moorish Spain followed by hundreds of years of the Reconquista, and parallel Christian-Muslim proxy wars in the Balkans (most notable for creating Vlad the Impaler, the model for Dracula, who due to events in his life played both sides of the conflict as it suited him), and in the Crusades in the Levant.
This would ebb and flow, however, as exogenous forces in the competing countries waging the proxy fights are able to devote more or less attention to the conflict. Infusions of resources from the proxy fighters keep the conflict going despite the limited capacity of the focal point of the conflict to maintain it otherwise.
There have been long running, near genocidal wars from coast to coast in the African Sahel for the entire post-Colonial period. At their root, these are being driven by global warming, which is slowly pushing the Sahel ecological zone previous occupied by Muslim herders to the South into Christian/animist marginal farmers in the next ecological zone to the South (who are less flexible and mobile since they own only the land that they own and are struggling as that land becomes less viable to farm upon) as the Sahara desert expands.
While particular groups in particular countries along that swath of Africa can make peace or have it imposed upon them for a little while, ultimately, it is an inevitable and existential fight between two ethnically and religiously distinct communities with different culture who have different means of food production and "business models" that are incompatible with each other and with the status quo. You can't herd and farm in the same place.
This wouldn't be stable, however, because while climate change means a long term steady trend in one direction, weather inevitably shifts on short and medium term scales, so two steps in the direction of the long term change are followed by one back in the other direction. Factors like major weather systems (El Nino type systems) and volcanic eruptions, can interrupt the long term trends in the short run.
Your world wouldn't have to have an expanding desert. It could be getting steadily colder (e.g. ice ages), hotter, drier, more moist, windier, or anything else you could care to mention.
Pandemics and Droughts and Floods
Major disease outbreaks like small pox and the black plague tend to be devastating for several years, then die down for a few years, then come back with a vengeance, over time frames that can last decades or centuries before they entirely run their course.
Pandemics, major floods (see China), catastrophic storm damages (see South Asia), and droughts often lead to civilizational collapses, that then usher in "barbarian" invasions of societies better suited to weak states and poor food production. When these disruptors ease up, however, society gets its act together a bit, drives off the barbarians or assimilates them and has a fragile new civilization until another disruptor screws it up again.
There is debate over whether some of the periodic disruptors on Earth are caused by our solar system's period trips through unfavorable parts of its larger area of the galaxy environment and comet routes, etc. But whether that does or does not happen on the real Earth, it certainly could drive these kind of periodic disruptors at scales that would be tough for even technologically advanced civilizations to handle.
Civilizational collapses of the Ancient Puebloans, the Mayans, the Incas, and the Mississippian peoples in the Americas are examples of that in the New World. Bronze Age collapse (ca. 1200 BCE), the fall of the Roman Empire (ca. 450 CE) and an earlier civilization collapsing arid period ca. 2000 BCE are examples of this kind of model.
Monarchies and colonial empires rely on "rent based" economies like farming and mineral exploitation (e.g. oil and gas) or natural resource exploitation (e.g. lumber, "spice") to survive.
Economies that are not "rent based" require the consent of the class of people who generate wealth (e.g. a diverse commercial and industrial sector) to function and tend to overthrow monarchies.
If you start with a monarchy or colonial system and the economic viable of its source of rents becomes minor relative to other sources of economic wealth in the economy, revolution sooner or later, is inevitable.
The revolutions and instability strike at the marginal point when neither the rents that supported the monarchy, nor the commercial and industrial economy that replaced that, is dominant, and when "current events" can upset the balance in one direction or the other.
For example, the invention of the cotton gin, and of industries powered by water mills and coal and steam, meant that sooner or later, the American slave based plantation farming system of the American South in the 1800s was going to collapse eventually. But lots of factors influenced when and how this happened and could have led to an oscillation if something got in the way of that trend.
Every country that has undergone economic development sees at least one and usually several regime changes near that margin of transition from undeveloped and resource based to an industrial economy.
Side Issue On Timelines and Long Term Conflict Mortality
A classic trope in media is the country that is constantly having a
revolution, with the logical extreme being a geographical region where
any map older than a year is woefully out of date as new nations rise,
borders shift, old nations fall and more coups are had than courses at
the following inaugural banquets
While maps change rapidly, there is a pretty much inevitable tradeoff between how long the conflict endures and how rapidly things change. If the situation is so dynamic that maps are changing in the region every year or two, the conflict is going to resolve itself in less than a decade or two. If you want a conflict that endures for half a century or a century, for example, while there is going to be significant change from time to time (and even that tends to happen in synchronized waves followed by periods of stagnation and stalemate) the conflict isn't going to progress quite that fast.
However, I want to be able to explain how this region manages to stay
so politically active when every settlement in the area would have
lost their entire population of 20-40 year olds after about ten years.
While you can have a world like that, there is really no precedent for that level of devastation happening that quickly as a result of war.
Most people who die in this eras aren't battle field casualties but casualties of the breakdown of civilization including war induced famine and disease that make the age breakdown of deaths more spread out. And, there are pretty much no historical military conflicts that killed more people than, for example, the Great Northern War over twenty years (which was a proxy conflict) in Finland in the 18th century that reduced Finland's population by about 50% and was followed by several other major conflicts in the 18th century that reduced the population somewhat further (but again, not primarily from battle deaths of military aged men).
Basically, people surrender no matter what the cost, or become refugees, before an entire generation of men is entirely eliminated, and conflicts that have that depth of impact take more than a decade.
You generally only lose an entire generation of men in historical scenarios of conquest, akin to those described in the Biblical books of Judges and Numbers, or in parts of the New World in the Conquistador era, for example, where an invading Army kills all the men and all of the women unfailingly loyal to them, and then the invading Army takes the remaining existing women as wives replacing the existing men entirely but taking their place, rather than leaving a vacuum.
Also, it is worth noting, that major wars like these generally lead to very high childbirth rates, approaching biological limits, although it is a less strong factor in leading to polygamy than you might naively expect (see, e.g., the case of very high rates of monogamy or non-remarriage among Southern Civil War widows even in communities losing a very large share of their marriage aged men).
I've touched on lots of big picture interpretations at a very high level of historical events as examples. But, for these purposes, the accuracy of those interpretations doesn't matter. What matters is that those interpretations could explain what is going on in your world.