But Robert Peck, curator of art and artifacts at the Academy of Natural Sciences, decided to give it one last try.
What he and Eric Newman, a numismatic historian from St. Louis, found has rocked the world of Audubon scholars, who are calling their discovery "a eureka moment."
Their quest began about a decade ago, when Newman visited the academy as part of a tour of libraries and important collections. He and Peck met. They had lunch.
A year later, Peck wrote to him. Had Newman ever seen a New Jersey banknote with a bird on it?
Newman was an expert on the early paper currency of America and had written a definitive work on the subject. He didn't know of any, but he began looking.
Meanwhile, Peck investigated the Audubon side of the mystery.
That first diary reference had been on July 12, 1824. Audubon had since moved from Mill Grove, but he was back in Philadelphia to garner support - from the academy, the preeminent scientific institution in the country at that point - for his bird watercolors.
That never happened, due to what historians contend were jealousies involving another bird artist, Alexander Wilson.
But Audubon wrote that "I drew for Mr. Fairman a small grouse to be on a banknote belonging to the State of New-Jersey."
"Mr. Fairman" would have been Gideon Fairman, a principal in a Philadelphia engraving firm that specialized in making paper currency for financial institutions.
At that time, each bank made its own currency.
On a trip to Chicago, Peck checked another diary, and found an entry from 1826. Audubon was in England, where his landmark book, The Birds of America, with full-size printings of his bird watercolors, was eventually produced, beginning in 1827.
He noted that he presented a friend "with a copy of Fairman's Engraving of [my] Bank Note Plate."
But had the money ever been printed? Or was it a plate that never got used?
Newman combed through every book written on New Jersey paper money. "That didn't help me at all," he said.
Then he checked the 10,000 different banknotes issued in the United States for grouse pictures. "I couldn't find any."
Finally, he reexamined his own collection of "sample sheets," printed with various images that bank presidents might want on their bills.
Mostly, such sheets contain portraits of George Washington and Thomas Jefferson, images of draped Lady Liberties, and, above all, eagles.
But finally, on a sheet issued by Fairman's firm, likely in 1825 - there! on the lower right! - was a grouse.
As was typical, the image wasn't signed. But while other wildlife artists of the day were producing static images, this had unmistakable Audubon touches - the unusual choice of species, the running posture that revealed a knowledge of the bird in the field, and hints of its grassy habitat.
"All the circumstantial evidence lines up," Peck said. "He writes in diary twice he did this drawing for Fairman. And that it was of a grouse. And that it was for a New Jersey banknote.
"And here, suddenly within months of Audubon saying he gave it to Fairman, the grouse appears on one of Fairman's sample sheets."
More searches led to more tidbits.
Eventually, Peck and Newman put together a likely scenario: Bills may have been printed for the New Jersey institution, the State Bank at Trenton, which employed Fairman's firm to design and print many of its bills.
But the bank began to fail in July 1825, and its notes were worthless by 1826.
Meanwhile, the State Bank of Camden had issued bills similar to the Trenton notes and also printed by Fairman.
In those days, with so many small banks and so much different currency, conditions were ripe for counterfeiting. Forgers altered Trenton notes to look like Camden notes.
The Camden bank eventually recalled its currency and burned it along with bills from the Trenton bank.
"The failure and scandal . . . all that is documented as part of banking history," Peck said. Whether the burned notes actually contained Audubon's grouse is likely, given the timing, he said, but unproven.
Peck and Newman also found later designs with Audubon's grouse - a $3 note for the Bank of Norwalk in Ohio and a $5 note for the Bridgeport Bank in Connecticut. But there's no evidence that either bank followed through and printed the bills.
The academy announced Peck and Newman's findings Thursday. They're being published in the fall journal of the Society of Historians of the Early American Republic, based at the Library Company of Philadelphia.
As word got out, scholars began calling with congratulations - and more tidbits.
"It's been one of the holy grails for Audubon researchers, to find out if that exists," said Nancy Powell, curator of collections and exhibitions at Mill Grove. Now, "it lets us know a little more about him and his art and how he developed it."
"It's the eureka moment where you find that missing piece of the puzzle," said Roberta Olson, curator of drawings at the New York Historical Society.
The society has all 435 original watercolors for Audubon's Birds of America. One is of a similar grouse - the pinnated grouse - and the society dates it to 1824, the same year Audubon supposedly made the image for Fairman.
To Olson, everything fits. Other wildlife artists of the day had found that making drawings for banknotes gave them not only money to live on but a certain cachet. So why not Audubon?
Peck said he thought Audubon's little grouse drawing worked against him. To be sure, it was different from all the eagles, and was not the sort of thing counterfeiters might use or copy. It also showed his prowess as an ornithologist, something he longed for in the stuffy Philadelphia science world that had rejected him.
But the grouse was, in a word, odd.
Bank managers who wanted emblems of security, nationalism, or patriotism might have shied away from it.
"A skittish grouse known for its shy behavior, and running, would not instill in the customer a great sense of confidence," Peck said. "But Audubon was so swept up in his own love of birds and his knowledge of their intimate behavior."
Peck and Newman know they may never learn the whole story. So much is gone.
The engraver went out of business in 1830. The Trenton and Camden banks failed.
The birds - also known as heath hens - have gone extinct. It's yet another detail that resonates among scholars of Audubon, whom many credit with the birth of the conservation movement in this country.
But neither Peck nor Newman can resist the tantalizing possibility that banknotes with Audubon's grouse on them were printed and still exist . . . somewhere.
Given the Trenton and Camden bank connections, they can't help but imagine some tucked away in a Philadelphia attic or stuffed into a Camden wall for insulation.
"That is always possible," Newman said. "Always."
Contact staff writer Sandy Bauers at 215-854-5147 or email@example.com.