Senescence

adj. Growing old; decaying with the lapse of time.

It is by a blend of lively curiosity and intelligent selfishness that the artists who wish to mature late, who feel too old to die, the Goethes, Tolstoys, Voltaires, Titians and Verdis, reach a fruitful senescence.
— Cyril Connolly, Enemies of Promise (1938)

Senescence begins
And middle age ends
The day your descendents
Outnumber your friends.
— Ogden Nash, Crossing The Border

Etymology
Latin senescere, easy to remember as the same origin as senile and senator.