Sophistication, freedom, rebellion or just the simple joy of taking to the open road with the wind in your hair. The convertible car used to represent all of these. But over the past two decades sales have collapsed, and its future seems deeply uncertain. So what's gone wrong?

In the 1950s and 60s, owning a convertible showed you had style. They were what the celebrities of the era were seen in.

When Hollywood deities Grace Kelly and Cary Grant were shown cruising along the French Riviera in a beautiful, sleek Sunbeam Alpine in To Catch a Thief, for example, they epitomised silver-screen elegance and savoir-faire.

Later films like The Graduate and Thelma and Louise helped cement the open top car's position as a symbol of escapism and rebellion for new generations.

For a while, convertibles were what people dreamed of buying, and manufacturers were happy to make them.

Yet today, the convertible is looking like an endangered species in the UK.

Over the past 20 years, sales of new open-tops have fallen by nearly 90%, from 109,171 in 2005 to just 11,484 last year, according to the Society of Motor Manufacturers and Traders.

That decline has coincided with a dramatic rise in Sports Utility Vehicles, or SUVs – large cars with at least a passing resemblance to four-wheel-drive off road vehicles. Last year they accounted for 59% of car sales across Europe, according to the research company Dataforce GmbH.

SUVs certainly have the kind of celebrity endorsement convertibles used to enjoy. Big is also bling, and today upmarket models such as the Lamborghini Urus, the Mercedes-Benz G Wagon or the Bentley Bentayga are widely favoured by today's reality TV stars, footballers and music artists.

What SUVs offer is some of the style and image of a convertible without the limitations an open top car creates, says Steve Fowler – a leading automotive journalist and founder of the car review website Carblah.

"It's a simple fact of people wanting more practicality these days," he explains. "I always say SUVs are sports cars for people who can't have sports cars any more. They've got that kind of image that perhaps a convertible used to have.

"And it's very difficult to put the kids, the dog, the bike, and everything else we have in our lives into a convertible."

Whether it's down to the rise of the SUV or not, demand for open top cars has fallen – and that makes manufacturers reluctant to build them.

"It costs so much money to build any car these days," explains Fowler. "And it's not just as simple as chopping the roof off...with safety regulations and everything else, you know there's a lot of work that goes into building a convertible."

Philip Nothard, insight director of Cox Automotive Europe agrees. "It's a very clear supply and demand marketplace," he says. "Convertibles are more expensive to manufacture, for a very small market share".

One consequence of this is that there are now relatively few convertible models on the market, and those that are available tend to be upmarket designs, because these offer higher profit margins.

The Mazda MX-5, the Mini Convertible and the Fiat 500 are exceptions, but customers looking for affordable soft-tops now have few options.

Nevertheless, the open top car still has its devoted fans.

"It's the nearest thing I can get to a motorcycle," says former biker Peter West, who drives a 2014 Mazda MX-5

"It's the sense of freedom. When you're in traffic you can hear the birds...it's just the driving experience."

"Everyone's too focused on SUVs these days," says Steve Bassett. Like Peter, he's a stalwart member Yorkshire Ridings branch of the MX-5 Owners Club. "I think people should be able to come back to the simple, elegant roadster".

Will they make a comeback?

It is important to remember that the last rites for the convertible have been read before. In the 1970s and 1980s, for example, sales plummeted as stricter safety restrictions made them more expensive to build, while consumer tastes moved towards high-performance hatchbacks. The increasing prevalence of air conditioning, meanwhile, took away part of the convertible's USP.

Yet ultimately, sales did recover and hit new records in the early 2000s. So do convertibles have a future now? According to Philip Nothard, that will depend on getting manufacturing costs down, at a time when the auto industry is heavily focused on developing electric cars.

The manufacturers most likely to do this, he thinks, are the Chinese firms currently moving into the market.

"They can manufacture vehicles at much lower cost," he says. "So if you're someone who's passionate about convertibles and you want to see affordable models, It might be best to wait for the Chinese to take a bigger slice of the market."

There are currently only two convertible electric models on sale in the UK, and one of those is indeed built in China.

The MG Cyberster is a sleek, open-topped two-seater that appears to have been designed specifically to exploit the heritage of the once-British MG brand, famous for roadsters such as the MGA and MGB.

The question now is whether it remains merely a digital throwback to the past, or heralds a new era of wind in the hair motoring.