HONG KONG — Whenever China’s economy swooned in recent downturns, its currency never buckled. It held steady, or strengthened, even as China’s neighbors or trading partners scrambled to cut the value of their own currencies to deal with the fallout.

With the Chinese renminbi now taking its biggest plunge in decades, the worry is that the country’s already slowing economy is even worse off than reported and that the government is panicking. On Thursday, China allowed the renminbi to weaken significantly for a third consecutive day.

The situation is shaking the aura of supremacy surrounding President Xi Jinping and the Communist Party, which has portrayed a sense of ultimate authority. But the Chinese government’s response to the country’s financial woes is creating concerns about its ability to manage a slowdown.

“People are used to growth and rising living standards,” said Jonathan Fenby, an author and co-founder of the research firm Trusted Sources. “But now they are in a ‘real’ world, and the leadership has to convince them both that slower growth is in their long-term interests and that it is in control.”