"And lastly, seated on some of the back benches, where they had
already taken up their positions for the evening, were divers
unmarried ladies past their grand climacteric, who, not dancing
because there were no partners for them, and not playing cards
lest they should be set down as irretrievably single, were in the
favourable situation of being able to abuse everybody without
reflecting on themselves. "

Climacteric
(a.) Relating to a climacteric; critical.
(n.) A period in human life in which some great change is supposed to take place in the constitution. The critical periods are thought by some to be the years produced by multiplying 7 into the odd numbers 3, 5, 7, and 9; to which others add the 81st year.
(n.) Any critical period.

So it's not just result of failure to secrete homones.

Oh, this is a great word, wwh, because it is very significant for several reasons. For one, climacteric shares the same Gk. root, klimax, that climax does. I think it helps young students to understand that the climax of a drama is often the turning point. The visual image of the action moving up a ladder (Gk. klimax) reaching the peak of the ladder and then coming down after the peak (or top of the ladder) helps. There are various types of climaxes, depending upon the subject, but the ladder as an image works.

Now about this climacteric that shares the same Greek root meaning ladder: I read that one of the definitions is the point at which fruit rises to its peak respiration rate just before full ripening.