By JAMES R. HAGERTY

PITTSBURGH—As architectural landmarks go, it’s hardly the Taj Mahal. It looks like a giant steel turtle bolted into a hillside, surrounded by parking lots and highways. The roof resembles an overturned mixing bowl. And its big pop-culture moment came when it was nearly blown up in Jean-Claude Van Damme’s “Sudden Death.”

It’s Pittsburgh’s Civic Arena, and if the Penguins hockey team has its way, the stadium will soon be torn down to make way for office buildings, shops and apartments.

The team, co-owned by supermarket mogul Ron Burkle and former Penguin star Mario Lemieux, has an option to acquire the land under the arena. Since the Penguins moved to the new glass-and-brick Consol Energy Center last year, the team says the abandoned Civic Arena has to go—it’s sitting on top of potentially lucrative real estate.

Rob Pfaffmann disagrees. The local architect, together with a small band of preservationists, is fighting to keep what he calls “Pittsburgh’s Parthenon” standing. They tout the arena as an iconic engineering marvel, featuring a retractable roof made of eight motorized stainless-steel leaves. Since it hasn’t been fully opened in more than 15 years, though, no one knows for sure if the roof still opens.

The Civic Arena

They point to all it’s given Pittsburghers: a Beatles concert, Billie Jean King tennis matches, some of the greatest hockey games of all time—including the one in 1989 when Mr. Lemieux had five goals and three assists against the Philadelphia Flyers. “Like a good comfortable shoe, it’s done its job,” says Franklin Toker, an architectural historian at the University of Pittsburgh, of the arena. Mr. Toker recalls the “thrilling experience” of watching the roof open during a Beach Boys concert more than two decades ago.

The Penguins see it differently. “It’s had its useful life,” says Travis Williams, a senior vice president for the team. “At some point, you have to move on.”

“What’s the rush?” asks Mr. Pfaffmann. He and his group say if the building is salvaged, even greater glories lie ahead. It could be turned into a park and amphitheater, for example. Others have proposed making it into a light-rail station, parking garage, water park, reflecting pool, roller-derby rink or greenhouse. At the very least, some say, the city should preserve the arena’s giant metal supports as a site for bungee jumping.

Preservationists in other cities have found it hard to save hallowed sports venues when teams move to glitzier homes. In Buffalo, N.Y., the cavernous Memorial Auditorium, affectionately known as the “Aud,” stood empty for 13 years, attracting vandals and graffiti artists, before being torn down in 2009. A plan to turn it into a giant sporting-goods store didn’t pan out. In Detroit, the old Tiger Stadium remained empty for a decade while politicians and preservationists debated such ideas as making it into a museum. It was finally razed two years ago.

In Pittsburgh, preservationists fear the Penguins’ plan will lead to a humdrum collection of chain restaurants, stores and hotels with no connection to local history. Mr. Pfaffmann’s “Reuse the Igloo,” group—after the arena’s local nickname—is asking the City Council to declare the site a historic landmark, blocking demolition.

But the local Historic Review Commission, which advises the council, rejected that idea earlier this month after that body’s chairman described the arena as “not something that should be celebrated.”

The issue is heading for the city’s Planning Commission on March 22 and will later be decided by the council. Mayor Luke Ravenstahl favors demolition, according to his spokeswoman. He and the Penguins’ management both argue that potential developers need a blank slate and wouldn’t want to work around a quirky old dome.

The arena’s designers might be dismayed to hear that. When it was being planned in the 1950s, a brochure said it would “take its place among the wonders of the world,” with “a majestic dome-shaped roof of gleaming metal which can be opened to the stars.” One magazine headline read: “Pittsburgh: Setting The Pace For Tomorrow’s City.”

The arena remains one of the few buildings of its era with a retractable roof. “Stadiums of the mid-century are some of the most endangered structures in the U.S.,” along with small motels, says Christine Madrid French, director of Modernism at the National Trust for Historic Preservation in San Francisco.

But the arena was also part of a now widely reviled urban-renewal program that included a freeway roaring through downtown Pittsburgh and boxy concrete buildings that haven’t aged well. And while the design did get some attention, locals complained that the city failed to follow through on promised jobs and housing for the surrounding Hill District. Some 8,500 mostly African-American residents of what was once known as Little Harlem were displaced by construction of the arena.

In its early years, the arena was home to the Civic Light Opera. But wind blew down scenery and created roaring sounds in the microphones when the retractable roof was opened. The opera company soon moved to other stages, leaving the arena to the Penguins.

The logistical problems continued. “Leaks were a big issue,” says Jay Roberts, a former general manager of the arena. Even though it was kept shut, the roof leaked. During a basketball game several years ago, the staff had to rig a plastic tarp from the ceiling to prevent rain from falling on the court. In the spring, during Stanley Cup finals, the air conditioning system wasn’t strong enough to keep the ice sufficiently hard. Corporate suites added long after the original construction had to be “sardined in” near the roof, Mr. Roberts says.

Opening the roof after all this time might be tough. One problem is that hundreds of cables—used for sound and lighting equipment—dangle from the ceiling. It would take days just to remove the cables before the roof-opening gear could be tested, says Mr. Roberts.

And then there’s the question of what happens next. In the past, Mr. Roberts says, the roof sometimes got stuck after being opened: “Every time you opened it, you wondered: Will it close?”

Write to James R. Hagerty at bob.hagerty@wsj.com