Julie Cohn was fully immunized when she went to her 12-year-old son’s basketball game in March. He requested that his mask be removed halfway through the match because he was getting too hot. She didn’t think much of it. He had a sore throat three days later. He tested positive for the coronavirus a few days later, as did his younger brother. Ms. Cohn cared for them, believing she was safe, but on March 28, she awoke with what appeared to be a head cold. She, too, tested positive the next day.

There is no perfect vaccine, and so-called breakthrough infections after coronavirus vaccination are uncommon and unlikely to result in serious illness. Federal health officials have told fully vaccinated people that they no longer need to wear masks or maintain social distance because they are protected, nor do they need to be tested or quarantined after an exposure, unless symptoms develop. The Centers for Disease Control and Prevention has now stopped looking into breakthrough infections in fully vaccinated people unless they become so ill that they need to be hospitalized or die.

Earlier this year, the agency was keeping a close eye on all cases. According to a C.D.C. report issued on Tuesday, the C.D.C. had received 10,262 reports of breakthrough infections from 46 states and territories through the end of April, when some 101 million Americans had been vaccinated, a number that was very likely “a substantial undercount.”

Only 555, or about 5%, of the reported breakthrough cases could be subjected to genomic sequencing. Over half of them involved so-called concern variants, such as the B.1.1.7 and B.1.351 variants. According to the new study, 995 people were hospitalized and 160 died, though not always as a result of Covid-19. The average age of those who died was 82 years old.

Some scientists agree that focusing on the illnesses that kill people, tax hospitals, and overwhelm the health-care system is a good idea. Nonetheless, the move has sparked debate. Critics argue that the agency is passing up an important opportunity to learn about the real-world effectiveness of the various vaccines and gather data that could help identify trends in the pandemic’s trajectory, such as how long vaccine protection lasts, how different vaccines compare in preventing infection with variants, or whether certain patients, such as the elderly, are more susceptible.

When asked to explain the change, a C.D.C. spokeswoman stated that no vaccine is 100% effective, but that the number of Covid-19 cases in fully vaccinated people is small, and that no significant demographic trends have been identified. The change means that the agency will continue to investigate cases such as the death of a vaccinated resident of a Kentucky nursing home, but not the infections of more than 20 other vaccinated residents and employees at the same facility who did not require hospitalization.

Some private health care systems are also researching vaccination failures among employees, which will provide useful data, she said, though such studies are not always indicative of broader trends.

However, even mild cases of Covid-19 can cause long-term health problems, and it will be difficult to determine the full scope without tracking mild infections as well. Ms. Cohn was not admitted to the hospital, but she did experience body aches, chills, and digestive issues for about two weeks. She was left with severe fatigue, headaches, brain fog, and vertigo, which caused her to crash her car into the garage one day.

Another reason for tracking all breakthrough infections is that they are unlikely to result in further virus spread. However, some experts argue that the scientific evidence is inconclusive.

Diana Berrent, the founder of Survivor Corps, a group of people who have Covid-19, has advocated for the creation of a national registry of all people with Covid-19, including those with mild or asymptomatic cases, in order to collect as much data as possible for future research.

Many scientists agree that gathering more data is always preferable to gathering less data. “The virus is constantly changing, and we need to stay three steps ahead of it,” said Michael Kinch, an immunologist and associate vice chancellor of Washington University in St. Louis’ Centers for Research Innovation in Biotechnology.