Well if you've been doing for 40+ books, I can hardly be called perceptive for picking up on it. 
There has always been some of this in the game. Vis has always been an in setting element rather than just a game mechanic. I fell in love with ars magica when I read the laboratory chapter in the first edition book even back then the mechanics provided much richer descriptions than in other games.
Playing wizards in a setting that doesn't just ignore what magic is capable of, I guess. Story and Personality Flaws too. Buying power with forced stories for the win!
First of all, I want to state that my opinion applies to Fifth and to a lesser extent Fourth Editions specifically. I first met Ars Magica in ArM3 and there are some nice qualities there, but not the decisive ones IMO.
Beginning by what was actually present in ArM3, character creation is ambitious and, for the most part, very succesfull. Its one weakness is the steep learning curve. On the other hand, it has a good selection of basic archetypes (and presents them in a far less railroading way than those of other systems - The One Ring is terrible in this regard, and the White Wolf systems are generally just passable) and offers a nice set of choices for customizing characters from there. It may well be the one RPG where it does not feel like magic power is a standardized product, but rather a mysterious asset that is to a large extent dependent on the person using it.
Also present in ArM3, but presented in what to me looks like a very poor way, are the elements of Medieval (make it Mythic) Europe, which are always nice to lend authenticity to the tale and to widen the narrative elements that can be introduced (by narrator and players both). It is really helpful to be able to reference actual history and actual places; it makes for a scenario that is as detailed and nuanced as the groups feels confortable to have. In this regard, ArM4 and ArM5 are really leaps and bounds beyond the previous editions and arguably any other succesfull RPG in the market except perhaps Pendragon.
Then there is the concept of the Order of Hermes, which is a solution and a resource to so many different things. It gives a ready-made yet customizable and flexible social structure for the PCs to participate of. Again, much of its strength is in how much it can be customized and changed as seen fit. It is just as rigid and as stable as the story benefits from it being.
I also feel that there is a wise decision to largely keep the customizable approach along the current line. Most Sourcebooks are written by specialists on the respective subjects instead of simply filling needed roles. Most are, indeed, very much optional and made for flavor and depth, which is always nice, far nicer than being unable to run a campaign without a new book. It rewards the players and narrators by making them feel supported instead of pressured into consumption. In several places (e.g. HoHMC, House Criamon) it is made clear that the campaign is "owned" by the group, not by the publishers, and that is how it should be IMO.
Which brings me to the general (current, not necessarily always past) philosophy of presenting a product that is fertile for a certain kind of narrative and works towards allowing the solid growth, expansion and development of that niche instead of, so to speak, "dancing" in front of the buyers in order to draw immediate attention and motivate an impulse buy. There is far more of a mutual commitment between publisher and consumers than is usual in the hobby.
If I had to choose a central element, I suppose it would be "mage characters playing in troupe style in a modified Medieval Europe". But to me this philosophy (which I found lacking in ArM3) is even more important.
This is true, but they normally weren't specialists on the respective subjects before writing the book. Ars Magica authors do a lot of research.
In general, this is what we are trying to do (although impulse buys are also good, of course), so it is reassuring to see that at least some people think we are succeeding. Thank you.
I would retain the Order/Mythic Europe and the magic system only.
I tried to keep the list short
-TeFo combinations ('Create Fire' or 'Destroy Animal' - when this came out it was decades ahead - only now do otherrpgs start using words for gaming rather than numbers)
EDIT:
bad stuff:
@ Pralix: Ruining House Criamon in the 5th edition? I think the 5th edition saved House Criamon! The members are no more simple madmen, they are madmen by system!
(I love this house!)
Chiarina
Exalted has 'em, too! (I don't expect 3rd edition will, but.)
Pendragon has death in childbirth too...
And Traveller famously has death as a possibility in chargen.
To be fair, so does Ars Magica if you're doing aging rolls.
I like the references to Medieval Legend.
I also enjoy the concept of troupe play.
What this usually evolved into in my groups was having players play NPCs and the "Nobody Owns an NPC" philosophy.
[Roughly: When you create an NPC related to your character, you surrender control to the group, whoever portrays that character is portraying them the "correct" way, even if it seems odd at the time because people are complex and have hidden reasons. We'll work out the reasons later in play. Of course, if the whole rest of the group hates it, we can always veto it.]
I don't really care about the Houses, never have, but it is nice to have a shorthand.
I prefer to use watered-down medievalisms everyone is likely to know for the shorthand [Merlin, Morgana le Fey, Caesar, Simon Magus, Medea, Alexander the Great, Charlemagne, Templars, etc.] and then introduce more obscure or modified legends in specific adventures [those creatures who run the sun from Divine, migratory legends, characters from Gudrun and the Langobard cycle, stuff I fished out of Eco's Baudolino, etc.]
Many of my players have enjoyed the community feel of the stories I put together, comparing it to Medieval Little House on the Prairie or a soap opera with wizards, but that's just personal style.
It boils down to creativity. Most other systems don't allow magic users to create their own spells and magic items to any meaningful degree. Sure, you could wrangle a new spell in D&D by wrangling with your GM, but it's not exactly encouraged. Ars Magica makes it easy to be creative. You can easily have spells no one else has, magic items no one else has ever conceived of. Your familiar? Unique. Your laboratory? Unique.
That was certainly the big selling point when we discovered Ars Magica 25 years ago. Now, it is no longer unique though. There is Mage and the lesser known and more similar World Tree.
If you take spontaneous magic away, it is no longer Ars Magica.
The other big thing, which takes longer to appreciate, is the long term advancement rules, which I have not seen parallelled in other games. If you take that away, Ars Magica is no longer unique.
The troupe style is the third big feature. Since it is style and not feature, it is easily ignored in ArM play and easily copied in non-ArM play. That, I think, makes it less important as a defining feature. It is more important as a feature defined by Ars Magica than the other way around.
IMHO, that's a cliché, and not real fantasy games.
The covenant as a character is important, but it is not unique. Long term campaigns in Call of Cthulhu are commonly played with a covenant-like concept, where characters have to retire from insanity, but the group, with its library and treasures, persists.
Yes, very. Perhaps not uniquely so though.
It's beautiful, isn't it
It wouldn't be Ars Magica without the long time frames.
Probably true, though that depends heavily on your group/people in your area/your general gaming/social context. I know for a fact that it still gets invoked.
... because I myself invoked it just a few months ago, though that particular game was actively intended to be a parody.
Absolutely true. Though in my gaming-context, these metacharacters tend to be referred to as 'covenants', be they a noble family and it's holdings or the government agency everybody is working for - especially if everybody is stuck in the same field office.
...and we're back to your specific gaming context I'm afraid. I have personally never witnessed a long term CoC campaign - probably because CoC players in my gaming context have not traditionally done this.
In fact, some of them would consider the idea Anathema I'm sure.
Mythic Europe - playing against the backdrop of medieval Europe, with supernatural elements such as dragons, faeries, and such. The particular year doesn't matter, but play in some fantasy setting or in modern times or medieval China or historically-accurate Europe (with no magic) or whatever - and it won't be Ars Mgica. Could be a cool game, but not Ars Mgica.
Magic System - a well-defined Verb + Noun system, both to cast spells and to make magic items. It doesn't need to have the specific verbs/nouns, or to be too well-defined (ArM3 is much less defined - I haven't played earlier editions), but a huge part of Ars Magica for me is twiddling with the magic system to achieve the magic you want, in-game.
Seasonal, Learning-based Advancement - increasing skills/Arts with XP gained by training/learning the specific skill, over a long time-span. Including initiation into Mysteries, which again is spending considerable time to advance in-game in a skill gain ability in a way that makes sense. Makes characters and the way they're built up over time very different from other games. It can be switched to roll-to-improve method (as in ArM3), or have different skills, or have Yearly or Monthly advancement instead of Seasonal, or so on - and still be Ars Magica.
The initial attraction to Ars Magica for me was the synopsis of the magic system in a Dragon Magazine review of 3rd. ed. core rulebook circa 1992. The mention of improvising spells or "spontaneous magic" really appealed to me, and still does. I like the core mechanics and intuitive nomenclature for (most) abilities. These things, to me, are what make the game Ars Magica.
I've played ArM in time periods well before canon in Mythic Europe, well after canon in modern America (doing so with current saga), and even briefly converted my long-running AD&D2e world to ArM. It's still ArM if Tech/Form and Sponts are involved, IMO.
Up-thread a bit, someone (couldn't find just now for credit) mentioned that certain changes would make Ars Magica into GURPS. I would totally support a generic RPG engine based on the core mechanics of Ars Magica. Supplements could then be published for Mythic Europe (e.g. ArM6) and maybe Urban Fantasy, a hot genre currently. Heck, an Action Movie supplement based on Feng Shui could work as well, since Atlas owns that property already (and Feng Shui reads to me like it would play well with the Simple/Stress dice mechanics with no other changes, YMMV).
Atlas could even OGL that core system and let other interested publishers do supplements for Space Opera or Bug Hunt genres.
Some readers are probably thinking, "but does the world really need more RPG systems?" Maybe not, but it really needs more RPG systems based on quality mechanics. Bonus points if they're mechanics I already happen to like:)
For me, it's the points that @ezzelino mentions. The most essential and what makes Ars Magica 'Ars Magica' are:
I don't know enough to comment on whether the system is unMedieval or not, nor can I make a judgement on the "goofy Latin."
For me to evoke Mythic Europe in my Ars Magica games, I'll take something like the Crusader Goose from this Medieval Magazine article and use it as a way to demonstrate how the Medieval paradigm ( and the mindset of the community that populates my sagas ).
For me it's pretty much: