Montessori teaching, at least where we were in the 1980's was very big on "critical periods" for learning tasks. There is a sweet spot where a child can learn things with ease, but when the time is past, it's an uphill battle.
The strongest example is foreign languages, where everyone in America has dozens of examples of children who picked up a language they were exposed to without conscious effort, but teenagers are reduced to tears trying to learn German and adults don't even bother to try unless they absolutely have to. This is supposedly true of music, math, drawing, and penmanship as well, though less strongly. But I don't know that the evidence for any of those is that strong. Everyone is exposed to some music and some mathematics just by walking around, even if they aren't taught any at school, so I'm not sure it's a clear measurement. They would learn different aspects of music and math, not none at all, and this might be enough to build the proper brain structures.
Thoughts?
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It's true that, if certain sensory inputs are wholly removed early on (e.g. the kitten with an eye patch), then it's possible that the facility will never develop. But except for the case of cochlear implants, this has almost no relevance for humans.
In terms of language, the whole thing is 1) hopelessly vague (what does "native proficiency" mean, and do you mean spoken, heard, written, accent, idioms, cultural references, etc.) and 2) so full of confounding factors, that I don't think there's much "there" there. So, for example: how do you account for the fact that immigrant children are spending their whole time in school, learning, whereas the adults are working all day, with MAYBE a class at the end of the day? How about the difference that child immigrants simply have a longer exposure time, more years immersed in the language? Maybe the older teens and adults are just more able to assert themselves against doing something hard, or less willing to be embarrassed by public mistakes, or are doing more (other) hard things and have less free energy to struggle with a language, or have alternate coping mechanisms (like sticking to ethnic enclaves)? How do you account for different levels and types of motivation, between children and adults? What about people trying to maintain two languages, vs. those dropping their previous language? How do you explain adults who develop an accent in their first language, or even lose capability in it? What about people who can write flawlessly, but have a heavy accent (or vice versa)-- are they counted as fluent or not?
Speaking for myself: I pick up languages easily, just by hearing them--this, well into my 40s. I also start picking up a local accent in English, after a few days (my family says I "go native"), and I pick up jargon and oddball words/phrases like I pick up cockleburrs on my socks. That's not the most common thing, but then, according to the "critical stage" theory, it shouldn't be possible at all, nor am I anywhere near the only person I know who does this. I know quite a few English speakers who lived overseas for years, and the majority of them who immersed themselves in the language (lived off base, dated/married locals, etc.) became fluent very naturally.
There is some truth to say, though, that there is often a slow, downward trend in fluid intelligence (g) beginning in the late 30s or 40s-- this will affect language acquisition then, but it doesn't explain the weeping teenager in German class. (It's also offset by the larger amount of crystallized intelligence in older people.)
As for music: like you say, nobody is wholly isolated from music at any time. There's also the factor that none of us, even infants, are simply passive recipients of the environment. All of us elicit responses from our environment-- babies chortle and coo at adults who please them, toddlers and kids plead relentlessly for things they like, teenagers get books/watch YouTube/seek teachers, etc. That is, if music "resonates" with the baby or child, he/she will actively seek it out, reward (with smiles, laughter, thanks, etc.) adults who provide it, etc. I don't know how you could separate the "push" from the "pull" effect, in other words. (For example, people with perfect pitch find off notes physically uncomfortable, long before they have words to express it; people without perfect pitch may learn scales later, but it doesn't tie as tightly to a physical feeling of "rightness" or "wrongness", and so they are likely much less motivated by it.) There's also the question of loss of hearing acuity with age, and the shorter free time available for practice (and shorter total time with the instrument) among older people.
I wasn't taught any language but English in my extreme youth, then studied some Spanish, French, and German off and on from kindergarten through college. In recent years (I'm 60 now) I've picked up a smattering of other European languages by working with Project Gutenberg. I can't say I've noticed any real change in how hard it is to learn a language during that stretch of time. It's true that I think I've only ever met one person whose English was virtually without accent who began learning it as late as his teenage years. Some people retain an accent you could cut with a knife, and some only a pleasing lilt, but it's rare to learn to pass for a native speaker that late. Still, the difference between learning at 15 and learning at 50? I don't really see it. It seems to be more about immersion.
A few thoughts: (1) I knew a couple that decided that the husband would use one language with their child, from day one, and the wife would use another. Supposedly, as a toddler, the kid was doing well, speaking both (2) If your language doesn't have a particular sound [ie, Japanese with R] there's a point after which you'll have difficulty pronouncing it, in early childhood (3) Around 15 or so, you start to be able to grasp abstract concepts. Trying to teach algebra to a 5 year old just isn't going to work.
The most recent research in language acquisition suggests that most people need to start early if they want to sound like a native speaker when they speak, but other than that, we can't clearly say that age makes much difference. Laura explained a number of factors that can account for the perception that children learn easier than adults and why that perception may not be true.
Thirteen is the usual cutoff for accents, though there is a range, and a few people who learn to speak unaccented versions of a language. Henry Kissinger has a younger brother with no accent, for example.
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