I have had two goats live to 16, but did not breed from them in their teens - although they both came into season, and would have been happy to visit the male.
One of our smaller goats has bred every year, and she is 6 now. I did notice this year she did not get in kid as early as usual, but that may be down to her male, as he is 7 now. I would definitely carry on breeding from a female until her early teens if she looked well enough to do so.
As I said I have kept goats into their mid teens - they had given me kids for years, and therefore owed me nothing, so happy for them to live out their lives here.