While tie length, collar type, coat length (to some degree), and a few other details (commonality of hats and gloves), have changed, men's suits, it seems, have consisted of basically the same garments, in the same configuration, since at least my great-grandfather's time. You could wear a formal suit from a wedding today to a wedding in 1930 and not look too completely out of place (the style would be strange, but everyone would recognize it was a suit -- it wouldn't be like wearing a tailcoat and breeches).
It seems women's formal clothes have changed much more radically during this period (certainly they have gotten a lot racier, if nothing else), and men's formal clothes were much different, in say, the 18th or early-mid 19th century. Further, men's formal clothes changed much more frequently, it seems in the centuries before. Clothes were very different for say, Henry VIII than they were for Charles I. Or Am I imagining that?
Why has the standard three- (or two-) piece suit remained so resilient?
I would argue that they have. We'll start with your 125 ballpark figure which would take us back to around 1890. Formalwear of that time would be white tie. While it's true the dinner jacket (or tuxedo for Americans) had begun to appear, it was only among the most fashionable. It made its debut in the US in 1886. The dinner jacket was considered informal at the time. If you were wanting formal day wear then a morning suit was standard: grey trousers and waistcoat, swallowtail (or cutaway) coat. This pretty much continued through to the first world war.
From the 1920s social rules were relaxed, and the dinner jacket became the norm. At this point it was still a 3 piece item, as waistcoats were still the norm. Though at the time, as it was considered vulgar to take your jacket off during the evening, many waistcoats were backless (allowing for less heat retaining fabric).
With the change of fashion from double breasted to single breasted jackets the cummerbund took over from the waistcoat. Further to my comment before about taking off your jacket, since this is now pretty normal, full backed waistcoats have made a return to menswear, sometimes even in place of jackets entirely.
Today, turning up to an awards ceremony (even something like your local Rotary Club) most people are happy if you have a shirt and tie. Bigger name events you usually have to wear a suit but very few people will actually turn up in a dinner jacket (and fewer still even own one). Then of course there was that whole 70s thing with powder blue, white and brown suits being considered formal.
Few people today attend formal events so don't own formalwear. Even wearing a suit at a theatre performance is considered dressing up now. Yes white tie still exists, but it's rarely seen outside State dinners and you or I will likely never get closer than looking at the pictures.
Men's fashions have always changed at a slower pace than women's, and if something becomes used less frequently it stops changing at all.
For questions on the "why" of fashion I often turn to James Laver, who wrote in the middle of the 20th century. His "Taste and Fashion From the French Revolution to the Present Day" is my constant companion, and a very interesting and accessible take on the "whys" of why certain clothes become fashionable.
Martiantripod is completely correct about the chronology of 20th century evening wear. But before we get to 1890, we will go back to the middle of the 18th century, and the "Great Renunciation" of men's fashion. Before the 1780s, men did indeed wear fabulous colors, fabrics, laces, and jewelry as a means of showing their wealth, taste, and importance. The center of men's fashion in the Western world was, naturally, Paris.
By the middle of the 18th century, politics and fashion were combining towards the style of the English gentleman--simpler clothes in darker colors and plainer fabrics. Those men who admired the simpler life and political liberty of the English adopted their style of clothing. After the French revolution political safety and fashionable taste dictated a style adapted first from the peasantry, and then from the bourgeoisie (who had never gone in for lace, jewelry, and scarlet silks the way the aristocracy had).
We now turn to England, who became the leaders in men's fashion. With Beau Brummell (Regency arbiter of men's fashion) the renunciation of bright colors and loud fabrics is complete. After the Regency and 1830s, another form of masculine adornment is renounced--tight fitting clothes that show off the finer points of the male figure. Essentially, by the middle of the 19th century, men have renounced almost all sexual, wealth, and status* display in clothing and left it entirely to women. (Except, of course, for a few exceptions which we will get into below.**)
Laver writes "Men's dress, unlike women's has no natural tendency to change." (Laver's theory of fashion is that zones of erogenous interest shift with the times, and that fashions shift around the body to enhance, point out, and almost-but-not-quite reveal the fashionable zone of interest. So the implication is, since men have left off sexual display in fashion, there is no need for changing fashion.) "On the contrary, its natural tendency is to stereotype itself. It is perpetually crystallizing into a uniform. This maybe explained, perhaps, by noting that whereas even in modern times... a woman is first of all a woman, and then a typist or a mannequin or a film star... a man is first and foremost a lawyer, a banker, or a bricklayer, and only after that a man. In a word, man's function in the State is more important than his function in the home: he tends to adopt the uniform of a profession."
Laver continues with descriptions of men's uniforms--military, waiters, judges (in England), barristers, Guards of the Towers, etc., and notes that they change very slowly. He also describes the main trends in menswear over the 19th and 20th centuries, and notes that their main trend is towards increasing comfort and informality.
Now, although Laver does not specifically discuss sexual display in men's dress (his fashion-change theory is concerned mostly with women), he does discuss status/wealth/power display. My explication of men's sexual renunciation in dress is taken partly from feminist fashion historians. However, he does state that men's dress does not change according to his laws of fashion, and so the implication is that men's dress is not about erogenous interest. I think it's a pretty fitting theory myself.
*Of course a well-cut suit in fine wool, and an immaculate linen shirt and silk tie is a display of status, compared with the shabby suit of a poor clerk, or a working man's overall. However, it does not display nearly the same amount of status difference that an embroidered velvet jacket, silk breeches and stockings, lace collar and cuffs, high-heeled shoes, and loads of jewelry does.
**There was of course a brief period in the 1970s where men took up sexual display in dress, with more flamboyant colors and more fitted cuts. Notably the only male dress today that combines color, authority, and flattery to the male figure is the military dress uniform. And every nice girl loves a soldier.
This is a fascinating thread, and I have a tangential question:
What about the rest of the world?
Both the question and the answers seem to be about European fashion (and places where European fashion was the norm). What about Russia, China, Japan, India or the Mid East? Do concepts like "formal" even apply?
From what little experience I have, I can tell you that when it comes to traditional clothing in India, the line between formal and non-formal is quite blurred. I would say a better dichotomy would be "court fashion" vs the alternative, or "festival fashion" vs the alternative.
Again, I don't really know much about the subject. I'd love to see someone weigh in on the issue of formal wear in non-European contexts.
I mean, women's formal wear has pretty much stayed the same, too. A lot of dresses made today would not look out of place in the 1930s (John Galliano's bias cut gowns come to mind).
Casual/sports wear is a different story.
A similar question which may have some relevant answers: http://www.reddit.com/r/AskHistorians/comments/10m7wv/why_has_western_formal_dress_become_the_worlds/