The canonical example is fluency in an unfamiliar (spoken) language. Most people lose the ability to internalize a new language to the point of being able to 'think in the language' as opposed to 'translating in your head' past their tweens, although the skill of deliberately acquiring new languages is itself learnable, and of course improves with practice, but the ability to learn to speak a language 'natively' (not merely fluently) is lost by nearly all people even earlier.

However, more to the point of this discussion, this age-linked loss of ability or plasticity does not seem to apply to learning programming languages (it is fairly common that one's first programming language is successfully acquired well past that point, after all). I suspect this has something to do with differences between listening/speaking vs. reading/writing fluency.