The group’s donor base, though, goes far beyond the gun industry or conservative interest groups. Those whose contributions or pledges have exceeded $1 million in recent years include Dr. Arnold W. Goldschlager, a California cardiologist and game hunter, and Joseph R. Gregory, a Tennessee businessman who co-chairs the Ring of Freedom. Then there are smaller donors like an Arizona rheumatologist, a New Jersey restaurateur and a Georgia accountant. Such breadth has in the past helped the N.R.A. remain a daunting lobbying force, but now, in addition to resistance from donors like Mr. Dell’Aquila and some signs of wavering grass-roots support, the N.R.A. is facing an increasingly well-financed gun control movement.

Financial support is also weakening from some top gun manufacturers as sales have softened. Sturm, Ruger & Company — which once had a promotional campaign in which it donated $2 of every new gun purchase to the N.R.A. — directed $10 million to the N.R.A. in 2015 and 2016, but only $1.5 million over the following two years, according to securities filings. The gun maker, which did not comment, appears to be trimming costs after its revenue fell to its lowest point in a half-decade last year.

Shares in American Outdoor Brands have fallen nearly 70 percent from its high of three years ago, and the company said in its latest annual report that it cut donations to the N.R.A. by nearly $1 million in its most recent fiscal year, without revealing what it gave. (Two years earlier, the company reported donating $1.6 million to the N.R.A. over nine months.)

Mr. Petersen’s influence over the N.R.A. has not been fully understood. His foundation is run by GiGi Carleton, his longtime secretary. (The Petersens’ two sons died in a plane crash.) The legacy of Mr. Petersen, born to a mechanic, looms largest in automotive circles. He founded the Petersen Automotive Museum, a tourist attraction in Los Angeles that houses one of the most renowned car collections in the world.

He also collected more than 2,000 firearms. Those on display at the N.R.A. museum include 12 Gatling guns, a Civil War flare gun and a revolver with silver bullets for vampire hunting, as well as a shotgun gifted by the British royals to one of the shahs of Iran. Three shotguns known as the Invincibles, made by the defunct gun maker Parker Brothers, are said to together be worth more than $5 million. The Petersens’ two sons are remembered by their two .22-caliber rifles.

Mr. Petersen did not live quietly. He once said he liked to take his Lamborghini Espada, a sort of Italian version of a muscle car, on hunting trips.

“He was truly a man’s man,” Mr. LaPierre once said of Mr. Petersen, adding, “Every time I saw him he’d come up to me, he’d look me dead in the eye and he’d say, ‘So what are you doing to defend my guns?’”