The primary meaning of the answer to a maiden’s prayer is an eligible bachelor.

The earliest instance that I have found is from New York Day by Day, by the American columnist Oscar Odd ‘O. O.’ McIntyre (1884-1938), published in The Springfield Leader (Springfield, Missouri) of 8^th June 1926:

Paris, June 8.—There is a clinging chill lamp of an abandoned cellar about Paris homes. There is more rain than sunshine. I have found most of the days soggy on every visit. Parisians do not mind showers. Today I saw one of those answers to a maiden’s prayer—high heels, waspish coat, ballooning trousers and silk hat—stand for half an hour in a drizzle. When his lady came along he raised the umbrella that hung on his arm all the time and walked away. That may be a brand of French chivalry.

However, the notion of maidens seeking help by means of prayers appeared earlier. The following etching by George Moutard Woodward (circa 1765-1809) and Thomas Rowlandson (1757-1827) was published in London on 25^th July 1801; titled The maid of all-work’s prayer!!, it represents a pretty young woman wearing a cap tied under the chin and a checked apron, kneeling at a rough kitchen chair; on the left is a broom, on the right are a pail and a mop; her prayer is:

O All ye Household Gods who preside over cleanliness and good management, aid me in my arduous undertaking. Scrub away from me, I beseech ye, all false pride, and vain consequence, and brush me up to laudable exertion. Let the smoothing iron of good nature, give a polish to my countenance, and lather within me the soap-suds of innocence, so shall I appear white as a new washed shirt in the eyes of my master. Mop from him, O cleanly Deities, the foul water of wickedness, when he comes home late from the tavern, and cleanse him with the brick-dust of reformation, so shall I remain as chaste as the children in the Nursery; but if he is permitted to bear about him the roaring fire of iniquity, the pure flame of my virtue, may be obliged to give warning, and quit its place for ever!
Erect in my bosom, I beseech ye, a register-office for all good actions, so shall I boil-over with gratitude for the numerous favors you have cooked up for my acceptance: And should a handsome fellow servant gain the heart of your humble worshipper, may he be diligent, sober, and honest; shake us then together in the frying-pan of matrimony, that we may become fritters of purity, free from broils and dissensions, and fit to wait at the tables of the good and virtuous, and be as it were warming-pans to each other.
Let these be my wages, and I shall submit cheerfully to my labours, nor shall I breathe a sigh for greater liberty, but make my bed in peace and sleep contented.

image: The Metropolitan Museum of Art – New York

 

This is one of the original—and forgettable—poems composed for The Elizabeth-City Star and North-Carolina Eastern Intelligencer (Elizabeth City, North Carolina) by a certain Benjamin S. Bulfinch, published on 3^rd February 1827:

The Old Maid’s Prayer.

Ye gods! who sooths [sic] our every care,
Hear a dejected maidens [sic] prayer—
Pity a woman of sixty-three,
Let some young man her portion be!
Believe me, tho’ old age bewitches,
I never mean to wear the breeches;
Some handsome beau I yet may greet,
Whose ruby lips with mine will meet,
And if he takes me, I’ll be bold
To say, I do not wish to scold.
My youthful days have fled apace,
But yet, I have no wrinkled face;
My teeth are few, and eye sight dim,
But I’m divested of all whim—
If I obtain the esteem of men,
I’ll never be a fool again.

The phrase the answer to a maiden’s prayer has come to be used in the general sense of a miracle solution; for instance, the following is from Co-production threat to drama, published in The Stage and Television Today (London) on 9^th April 1992:

Leo Eaton, senior vice president for national and international productions at Maryland Public Television, told The Stage and Television Today that the massive increase in the number of channels and the subsequent disintegration of the commercial market would eventually force cash-strapped programme-makers to co-produce.
Eaton said: “A lot of people jumped into co-production thinking it was the answer to a maiden’s prayer – which it isn’t. But the fragmenting marketplace in the US and Europe will mean that we have to co-produce.”