American designer Ralph Lauren was the most recent departure when it announced last month that it was closing three of its stores in Buenos Aires, including its flagship in the upscale Recoleta district, as draconian measures on imports have all but left it unable to stock its shelves.

Ermenegildo Zegna, Escada, and Calvin Klein Underwear had already closed or reduced operations sharply in response to the growing challenges to doing business in the country. Local media outlets reported French jewelry boutique Cartier is planning to follow suit next month.

President Cristina Fernández late last year tightened controls on imports to protect a dwindling trade surplus. Her administration also restricted access to foreign currency to prevent growing ranks of Argentines from trading their pesos for U.S. dollars to protect their savings from one of the highest inflation rates in the world.

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Tourism, which has boomed in the past decade, has slowed down as Argentina became more expensive and many Europeans limited travel due to a tougher economic climate at home.

The moves underscore the growing difficulties facing foreign companies in Argentina, where the government has resorted to protectionism to address challenges such as soaring internal prices, a reduced confidence in its currency and an eroding trade surplus.

“It’s a complicated scenario,” says economist Miguel Kiguel, director of EconViews consultancy and a former Argentine finance secretary. “Companies can’t bring the products they need to function normally. On top of that, tourism has dwindled as the country became more expensive.”

For the city of Buenos Aires, sometimes referred to as the “Paris of Latin America,” losing blue-chip international brands is a blow to the city’s international flair.

“These stores are so elegant and glamorous,” said shopper Cristina Beltrame, walking down the Alvear Avenue, the most Parisian of Argentine streets in the Recoleta neighborhood, last weekend. “It’s sad to see them go.”

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Ralph Lauren said in a statement that the closing was temporary but did not specify if and when it planned to reopen its stores.

Argentina imposed controls last year after Central Bank currency reserves shrank by more than 10% as Argentines lined up in front of exchange houses to buy U.S. dollars. The country, which has been unable to tap international debt markets since its $95 billion debt default in 2001, needs the reserves to pay off debt.

The government has all but banned international companies from remitting profits overseas in a bid to reduce the demand for international currency. Argentines are also prevented from buying foreign currencies, forcing many to ditch their international travel plans ahead of the summer season.

The foreign currency controls and a growing sense of malaise, as the economy slows and inflation continues to erode purchasing power, have cut deeply into the popularity of President Fernandez. Local polling firm Management & Fit said 72% of Argentines currently disapprove of the way the government is managing the economy.

In response to the financial controls, perceived by many as a restriction of their personal freedoms, hundreds of thousands of Argentines took to the streets last week banging pots and pans and chanting against price increases and growing crime, in the biggest challenge to Fernandez presidency in more than four years.

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While the President tried to play down the importance of the demonstration, local analysts view it as a watershed moment in her presidency.

“The middle class that demonstrated last week is a key social segment in the country’s political makeup,” says political analyst Rosendo Fraga. “And this protest shows that those voters are now distancing themselves from the government.”

Argentina’s economy is still on track to expand 2.2% this year, according to the World Bank, down from almost 9% in 2011.

Some companies, such as French apparel company Lacoste and Research in Motion (RIMM), the maker of the Blackberry smartphone, have set up local factories to produce or assemble some of their products in the country.

But for the large majority of international brands, the scale of the Argentine market does not warrant such a move, especially considering that the wages of local workers are the highest in the region.

One of the most controversial measures the government imposed last year was to require that companies importing products compensate with exports of their own, prompting unusual partnerships such as a luxury car makers teaming up with local wine exporters or a luxury brand retailer establishing a partnership with a wool-exporting company.

Carmakers Fiat and Renault this year both had to slow down production due to a shortage of imported parts.

The controls have left little choice for many international companies – a choice the Fernandez administration must have known would likely happen. So far, though, neither the departure of the global brands nor the dissatisfaction of the Argentine people is enough to matter.