The expression autumn-spring denotes a period of warm, springlike weather occurring in the autumn; hence, figuratively, a late period of youthfulness.
—Synonym: Indian summer.

The expression autumn-spring occurs, for example, as the translation of Babí Léto, the title of a 2001 Czech film directed by Vladimír Michálek (born 1956), starring Vlastimil Brodský (1920-2002). The following is from A Czech Legend In a Swan Song, by Dave Kehr, published in The New York Times (New York City, New York, USA) of Friday 22^nd August 2003:

In “Autumn Spring,” which opens today in Manhattan, the cuddly, avuncular Brodsky plays Frantisek Hana, a feisty 75-year-old former actor, who gets through the frustrations of forced retirement by playing harmless scams—pretending to be a world-famous musician shopping for a country villa or introducing himself to strangers as a long-lost friend.

The earliest occurrences of the expression autumn-spring that I have found are as follows, in chronological order—the first four are from books by the Anglican clergyman and historian Thomas Fuller (1608-1661):

1-: From The Historie of the Holy Warre (Cambridge: Printed by Thomas Buck, 1639):

And now the Christians began every where to build: The Templars fortified Gaza; King Richard repaired and walled Ptolemais, Porphyria, Joppa, and Askelon. But alas! this short prosperity, like an Autumne-spring, came too late and was gone too soon to bring any fruit to maturitie.

2-: From The constant Virgin, Chapter 12 of The Holy State (Cambridge: Printed by R. D. for John Williams, 1648):

God may justly desert people for snatching that to themselves, which is most proper for him to give, I mean, Continency. Object not, that thou wilt pray to him to take from thee all desire of marriage, it being madnesse to vow that one will not eat, and then pray to God that he may not be hungry. Neither say that now thou may’st presume on thy self, because thou art well stricken in years, for there may happen an autumne-spring in thy soul; and lust is an unmannerly guest, we know not how late in the evening of our lives it may intrude into us for a lodging.

3-: From Good Thoughts in Worse Times. Consisting of Personal Meditations, Scripture Observations, Meditations on the Times, Meditations on all kinde of Prayers, Occasional Meditations (London: Printed by W. B. for J. Williams, 1652):

Green when Grey.

In September I saw a Tree bearing Roses, whilest others of the same kinde, round about it, were barren; demanding the cause of the Gardener, why that Tree was an exception from the rule of the rest, this reason was rendered, because that alone being clipt close in May, was then hindered to spring and sprout, and therefore took this advantage by it self, to bud in Autumn.
Lord, if I were curb’d and snipp’d in my younger years by fear of my parents, from those vicious excrescencies, to which that age was subject, give me to have a godly jealousie over my heart, suspecting an Autumn-Spring, least corrupt nature, (which without thy restraining grace will have a Vent) break forth in my reduced years into youthfull vanity.

4-: From The best Act of Oblivion (London: Printed for John Stafford, 1655):

Beware therefore that in your old age ye be not guilty of the sins of youth. Gardiners can tell you, that when Rose-trees are clipt in the moneth of May, so that then they cannot bring Roses, they doe commonly bring them in the Autumn spring, in the month of September. And it is possible, if you have been restrained, either by sicknesse of body, or naturall modesty, or want of opportunity, or restraining grace, from the excrescencies of youth, when you are young, I say it is possible, that you may be visited with such guests in your old age, and make them welcome at your own perill.

5-: From a conversation between two Lords, in Loves Labyrinth: A Tragi-comedy, appended to Virtus Rediviva A Panegyrick On our late King CHARLES the I. &c. of ever blessed Memory (London: Printed by R. & W. Leybourn, for William Grantham, 1660), by Thomas Forde (fl. 1647-1661):

1 Lo. VVhat’s love in young, is dotage in old men.
2 Lo. Love can create an Autumn Spring, infuse
New spirits in the old, and make them young.