BEIJING — Even before the Olympic flame is extinguished in Rio de Janeiro, China is deep in debate about its showing in the Summer Games. Many Chinese are asking if the nation’s once insatiable appetite for medals has hit a limit.

China is vying to come in second in the gold medal tally, behind the United States and a bit ahead of Britain. While it has often finished second in the Games, China’s number of gold and overall medals is down considerably, especially in some sports in which it has been strong, generating angst in a country that is used to viewing its medal count as a measure of rising national power.

For many athletes and fans here, even the relatively minor slip in results has smarted.

“We definitely did not perform our best,” Liu Xuan, a retired Chinese gymnast who won a gold medal in the 2000 Olympics, said in a telephone interview, referring to the gymnastics squad. She complained about the judges, but acknowledged problems with the team’s preparations.