When David Groeger was 17 years old, his parents bought him a white, 1998 Mustang convertible as a birthday present.

"In high school, it was the coolest car that was," says Mr. Groeger, who grew up on Long Island, N.Y. "People knew me for that car."

People still do. Mr. Groeger, now a 32-year-old lawyer in Farmingdale, N.Y. still has that Mustang—even though, he says, "I've put as much money into keeping this car running as it would [cost] to buy a new one." Among the repair bills: about $5,000 spent to replace the engine after the original melted down on the New Jersey Turnpike three years ago. He also has replaced the canvas top—it was ripped and leaking—and had two vanity plates stolen, including one that read DAGSBABY.

Mark Jones, of Orinda, Calif., says his dog Rocco was the only family member still happy to ride in his dented 17-year-old Volvo.

"My really close friends would love to see me get a new car," he says. Members of his family "get worried about safety." But Mr. Groeger says he's sticking with his Mustang. Even when the engine died, he says, he couldn't bring himself to scrap his beloved "Sally."

So strong is the emotional bond, in fact, that he even had the car's pony logo tattooed prominently on his shoulder—which he says makes it tough to trade up.

"What do I do, get a Hyundai tattoo?"

Nearly half of the 250 million cars registered in the U.S. are now 11 years old or older, according to R.L. Polk & Co., an automotive-market data company. And while many people drive older cars because they can't afford a better vehicle, there are plenty who could ditch their old car or truck, but don't. They like the values an old car reflects—dependability, frugality, a rejection of a throwaway, planned-obsolescence culture. Old cars can remind their owners of youth, family and adventures. Some old cars are more than machines to their owners. They have personalities. They have names.

Nikki Montgomery of Wausau, Wis., says it feels as if her Pontiac Grand Prix 'was built for me.'

In a 2010 paper, researchers at the University of Michigan's psychology department found that subjects who were prompted to think of their cars in anthropomorphic, or humanizing, terms expressed hesitation about dumping an old one, even after they indicated it was unreliable.

"There are really strong norms against replacing people because they are no longer adequate," says Jesse Chandler, one of the paper's lead researchers, who now works for a public relations company in Ann Arbor, Mich. Transferring those feelings to cars, however, can mean paying for expensive repairs. Mr. Chandler says he is pursuing new research, looking at how interpersonal relationships affect the relationships people have with their cars.

A trusty vehicle can inspire fierce loyalty. Robert Hill and his wife, Andrea, have a 1985 Mercedes-Benz 380 SE—nickname: Brunhilde—that is still going strong after 190,000 miles. "We use that Mercedes like a rented donkey," says Mr. Hill, 64, a retired medical researcher who lives in Santa Rosa, Calif., and calls Brunhilde the best car he's ever owned. "I'm going to be buried in that car," he says.

Orlando Soria of West Hollywood, Calif., with his Toyota Prius, which he says he has no 'emotional connection' to. He says he wept when he finally gave up his old Volvo.

Alexander Edwards of Strategic Vision, Inc., a California-based market-research company, says his surveys find that people who keep a vehicle for more than 10 years tend to value comfort, reliability and security. "They're more likely to garden and go to coffee shops," he says, "and do home DIY projects." They're more likely than the average consumer to have libertarian political views, he says, and have little interest in luxury features—unless they have a practical purpose.

The average new-car buyer is now keeping a vehicle for nearly six years—up from almost four years on average in 2001, says Polk vice president Mark Seng. The rising longevity poses a dilemma for auto makers. On one hand, they like to showcase testimonials from customers about the durability of their cars. But the longer life span means the average consumer will buy only nine vehicles in a lifetime instead of 13, Mr. Seng says.

Nikki Montgomery, a morning radio show host at WDEZ in Wausau, Wis., says she doesn't plan to let go of her 2005 Pontiac Grand Prix any time soon, even though it has 180,000 miles on it—more than a decade's worth of driving, based on the national average of about 13,476 miles a year.

"The seats kind of hug you," Ms. Montgomery says. "I feel like the car is built for me." General Motors Co. GM -1.06% killed the Pontiac brand as part of its 2009-2010 bankruptcy, so Ms. Montgomery can't get a new Grand Prix.

Ms. Montgomery and her husband have a newer SUV, but she's attached to her old sedan, which she calls dependable and fuel efficient. But she says her husband has set a boundary for her relationship with the Grand Prix: "My husband said, 'No, you cannot name a car.'"

Parting with a beloved set of wheels can be an emotional jolt. Orlando Soria, 30, says he wept when he cleaned out his 1999 Volvo V70 before donating it to benefit National Public Radio last September. Mr. Soria, a West Hollywood, Calif., interior designer who works for HGTV and private clients, says the car had been part of his life since he was a junior in high school and reminded him of road trips with his parents. Among the artifacts discovered when he cleaned out the car were cassette tapes of Japanese lessons his mother had listened to during drives.

Giving away the Volvo, he says, was a "final goodbye to the end of your adolescence." As for his new Toyota Prius? "I have no emotional connection to it," he says. "I don't identify with it at all."

Clinging to a car isn't just about money. Here's what one automotive research firm discovered when it surveyed consumers who held on to their cars for 10-plus years:

They like to travel overseas
They look for security in their relationships
They have a college degree
They tend toward libertarian political views
They like to garden and do their own home repairs
Source: Strategic Vision, Inc.

Big repair bills for a blown engine or worn-out transmission are often what finally kill an old car, says J.J. Jobst, owner of Schaumburg Automedics, an independent repair shop in Schaumburg, Ill. The end can be emotional. "I've had people cry on me," he says, when he's delivered the news that saving an old car will cost more than it's worth. But Mr. Jobst says even a major repair can be less expensive than signing up for a new car payment, "if you're going to keep it for three or four years."

As chief executive of Vehicle Donation to Any Charity, which operates a car-donation program based in Point Richmond, Calif., Mark Jones has ample experience with people overly attached to a jalopy.

In fact, he's one of them, he says, having finally unloaded his Volvo 850 sedan just last month after 17 years of loyal service. The 53-year-old from Orinda, Calif., says he kept it because he likes to hang on to cars for a long time and "get my money's worth." He also asks, "Do we want to consume that much?"

He had offered the car to his teenage children to drive to school, telling them stories of his own adolescent adventures bombing around in a friend's 1963 Plymouth Valiant wagon. But his children complained they'd be embarrassed to roll up in his old Volvo to a parking lot filled with BMWs and newer cars. (It got to the point, he says, where the family dog Rocco was the only one who would happily ride with him.)

The end came when the radiator blew up, and his mechanic estimated the repair at $1,200. Mr. Jones says he almost chose to get the car fixed, but ultimately decided to let go. "I knew my family would kill me."

Corrections & Amplifications

Nikki Montgomery drives a Pontiac Grand Prix. A caption in a previous version of this story incorrectly identified her car as a Pontiac Grand Am.

Write to Joseph B. White at Joseph.White@wsj.com

A version of this article appeared March 13, 2013, on page D1 in the U.S. edition of The Wall Street Journal, with the headline: Breaking Up With a Broken-Down Car Is Hard to Do.