Again the probably obvious "correct" answer here is that it's because Narnia is a fantasy story set in a fantasy kingdom which conforms to the convention of fantasy literature (even if it probably did help to define alot of those conventions itself) and so it is set in a perpetual Middle Ages as per the genre.

However, perhaps some more interesting answers are as follows:

• Civilisations don't necessarily develop as fast as you might think - if you were to compare early Anglo Saxon Britain (500 AD) with the period of the Norman Conquest 500 years later (1066) and the War of the Roses another 400 years after that (1487) you would probably observe that combat is still predominantly fought by men on horseback with swords, and that England is mostly a land of hills and Castles, despite almost 1000 years passing.

• Civilisations develop at different rates - when English settlers first arrived in North America in around 1600 they encountered the Native American population which had barely changed its way of life in 1000s of years. History is full of these sorts of disparities across multiple continents.

• Societal development sometimes goes backwards - after the fall of the Roman empire, the development of society in Europe went very much backwards during the Dark Ages, and probably took 800 odd years or so to get back to where it had been. Narnia probably suffered a big hit from the 100 Year winter in this regard.

• Rapid technological advancement is a fairly recent thing - the Wright Brothers first flight was in 1903... 66 years later we put a man on the moon. That sort of rapid technological advancement was unheard of before the 20th Century.

• Narnia is a kingdom predominantly consisting of Animals - it probably goes without saying, but Animal societies, unlike human societies, have shown zero societal development since the dawn of time.

Calormen doesn't evolve either from what we see of its people. I guess Archenland and the Lone Islands might; we see so little of them. I believe C. S. Lewis really found the medieval culture aesthetically pleasing, more so than any other apparently. So for Narnia to be his ideal, it had to be frozen in time sort of. Plus it was probably easier to write and to get readers attached to it if he didn't have to reimagine it every couple of books or so.  

There is one way in which Narnia changes over the years. In Prince Caspian, we learn that there were only talking mice in Narnia after The Lion, the Witch and the Wardrobe and the talking elephants in The Magician's Nephew seem to have died out.

I wonder if Narnia had evolved, what would the Pevensies have done? 

Considering that if they ever thought about Narnia, it would be the Narnia they know. Although in PC they are faced with new problems, imagine if it had been new technology? Would they have been help at all? Especially since they don't know how to live in this new Narnia. 

Posted by: @kingedthejust

I wonder if Narnia had evolved, what would the Pevensies have done?

To put the 1300 year time gap between LWW and PC into perspective, that's the same amount of time between the reign of Tutankhamen and the reign of Cleopatra in Ancient Egypt, or the same amount of time between Alexander the Great and William the Conqueror in European warfare.

In either case, viewing such a 1300 year time gap from a future vantage point (2021 for me, 1941 for the Pevensies) the level of technological change would be easy to comprehend.

Even if Narnia had suddenly evolved to the point of Victorian industrialisation, the Pevensies would still have the benefit from being from a comparative future, and having the advantages of a school history education to know what the basics were.

Even if Narnia had evolved to a point that was now in the future (i.e technology in advance of 1941) all that really does is flip the genre from Fantasy to Sci-Fi, and I don't have any doubts imaging the children would be able to apply the same lessons of courage and ingenuity to deal with a sci-fi situation any less than a fantasy situation.

One reason for setting Narnia in a medieval-style world is that this gave the chance to show noble and worthy characters, including a number who live simple but honest lives. The values of chivalry translate well into Narnia, the loyalty, courage  and truthfulness shown by all the good beasts, the need for the children to take risks and fight for right. The wonder and joy and freedom, that are seen in Narnia when Aslan has played his part, are important.

But although the basic technology of Narnia does not change (ignoring the unexplained sewing machine, umbrella and so on in LWW) by  PC society has changed. The undesirable type of human has arrived, and has instituted a very mixed society of bullies and bullied. Miraz and his lords are ruling Narnia in a way never expected by the Old Narnians, who still manage to hold onto their memories of the good humans and their reign. At least they seem to have brought in superior crossbows, and not pistols. Fortunately not all Telmarines are evil (eg Lord Berne and many of the townspeople of Beruna).

Another possible reason for the medieval setting is that Lewis was, in fact, a Professor of Medieval Literature  

The series doesn't seem to take technological advancements very seriously, as has been pointed out (Coriakin even has a water pump, which I believe was an 18th century invention). We get the swords and castles where they're important to the larger than life, chivalric aspects of the stories, but otherwise little gadgets pop up here and there to remind us that it isn't homogeneously medieval.

@kingedthejust 

I don’t think Lewis would have wanted Narnia to have modern technology. He was more than satisfied with the medieval world, and that was mostly the model for Narnia.  So Narnia would not change very much except for the landscape, e.g., between The Lion, the Witch, and Wardrobe and Prince Caspian. Perhaps that is he wanted in our world- an old fashioned medieval type of place. Tolkien would probably have wanted the same thing.  It would be no cell phones or computers for either of them. 

@narnian78 

I actually appreciate that Lewis didn't change Narnia. I wouldn't have preferred it at all, because I like Narnia how it is. Yet I still tend to wonder what kind of 'modern technology' C.S Lewis would've created for Narnia, especially considering the books were written in the 1940's. Imagine if 'modern Narnia' is just some of the things we use in our daily lives! 

I wonder why he chose Medieval times to begin with. The animals in Narnia were living in times with kings and Queens and knights. The animals would have to adapt to having Modern Technology, just as much as they did having the Medieval times to live in. It's really just an interesting food for thought. 

This question honestly never occurred to me when I read the series.

It seems the highest technological level attained was the production of steel, for weapons. We can attribute that to the craftsmanship of the dwarves, with probably a magical component involved.

But, for technology to evolve, there needs to people, commerce, and the trading of ideas, and Narnia just didn't have that. Not least because there's a dearth of actual humans.

The most populous country seems to have been Calormen so any evolving would have been done there.

OT/ rant: I've read some books in Mercedes Lackey's Valdemar, and THAT place  holds to the Narnia tradition of not evolving either, while having 50X as much written about it!

Narnia had no need for radio or television since its inhabitants had Aslan to rely on for all they needed to know. They could do without cars and most other forms of modern transportation. I read somewhere that Lewis never learned to drive, which is something in our world which we find difficult to do without. Was it an advantage that Narnia may have been considered primitive in our world?

@narnian78 you've just shone a light on this for me. 

Lewis himself did not have radio or television. He didn't even read newspapers. His childhood love of medieval nobility and so on must be taken into consideration in this question. Not that he hated all machines, as he rode a bicycle and travelled as a passenger in cars, taxis, trains and boats. 

I think my final answer has to be that Narnia is Lewis's World. Perhaps, as with Bree the horse, it is the country of his childhood, and  he does not want modern things there. In these stories he has taken us readers into his own land. 

I don’t think would have Lewis would have been fond of movie and television versions of his books. He probably would not have hated them, but he wasn’t overly enthusiastic about technology.  Narnia evolving into a motion picture was not something that he loved very much.  If he were living today he might have just accepted that they would be made without liking the idea so much. Most of his readers may have disagreed with him on this since Narnia films and TV adaptations have been made and people like them.  The theater drama versions didn’t appeal to him so much either, but if he were living today he might have seen their presentation as a way of getting people to read his books.