BEIJING — Yu Xilin was obsessing on China’s plummeting stock market when he tumbled off his bicycle. But the accident did not sway his focus. While recovering in the hospital on Thursday from surgery for a broken ankle and shoulder, he was using his smartphone to track his shares.

“The government departments that are supposed to be monitoring the stock market aren’t doing their job properly,” Mr. Yu, 55, the director of a provincial cultural exchange office, said by phone from his hospital bed in the northwestern city of Xi’an. “This will affect the image of our leaders. Investors are very upset.”

Even if China’s stock markets end their dizzying falls — and analysts say there is still room to tumble even after a respite on Thursday — the sense of supreme control that once cloaked the Communist Party leadership may take longer to recover.

Across China, many of the millions of middle-class investors have been asking why the party and the government talked up the market in the months leading up to the recent plunge, and then bumbled in their efforts to prevent the rout.