Incidence of Reye's syndrome has fallen so sharply in the past two years that a federal study of the possible link between aspirin and the viral disease is having trouble finding enough cases to examine.

One reason for the decline may be that more and more parents are heeding health officials' warnings about the risk of giving aspirin to children with chicken pox, flu or flu-like illness.

Further evidence of a link between aspirin and Reye's syndrome, a rare but potentially fatal disease in children, is reported in the current New England Journal of Medicine. The study found that 28 of 30 children (93 percent) who developed Reye's syndrome after chicken pox or flu had taken aspirin. Among a comparable group of 145 children who had chicken pox or flu but did not develop Reye's, only 46 percent had taken aspirin during their illness.

A huge federal follow-up study to examine this possible link is now under way at more than 50 pediatric referral centers, including Children's Hospital in the District and the Johns Hopkins Children's Center in Baltimore.

Four previous studies since 1980 had reported that children who took aspirin for chicken pox or respiratory illnesses had an increased risk of Reye's syndrome. Those studies, which drew sharp criticism from the aspirin industry, led the U.S. surgeon general in 1982 to caution against automatically giving aspirin and aspirin-containing medicines to children with flu or chicken pox. The warning covers any painkiller or cough medicine containing salicylates -- a group of non-narcotic analgesics, the most common of which is aspirin. The aspirin substitute acetaminophen, sold as Tylenol and other brands, has not been linked to Reye's syndrome.

Since the first reports linking aspirin to Reye's syndrome, the number of reported cases of Reye's has dropped sharply, from 550 in 1980 to 204 last year. Fewer than 100 cases have been reported this year.

"Aspirin use is decreasing, and certainly that could be one explanation," says Dr. Michael Barrett, coauthor of the New England Journal study and medical epidemiologist at the Centers for Disease Control (CDC) in Atlanta. Another contributing factor, he says, could be a change in the viral strain of flu during the past two winters.

The decline in reported cases is not a reason to ignore warnings about aspirin use in children, Barrett says, particularly since the disease has not declined among teen-agers, who are more likely to take aspirin without their parents' knowledge.

"If anything," he says, "there's reason to strengthen that message to people."

The report in The New England Journal suggests a statistically significant "association" between Reye's syndrome and use of aspirin during a preceding illness.

But the Aspirin Foundation of America, an industry group, took issue with the latest report, saying there is no proof that aspirin causes Reye's syndrome.

"We don't feel there's any proof that there's any relationship between aspirin and Reye's ," says Dr. Joseph White, president and chairman of the foundation.

White says the study in The New England Journal was merely a feasibility study, from which "no conclusions can be drawn" about the relationship between aspirin and Reye's syndrome. Since the CDC has not released the underlying medical data, he says, the pharmaceutical industry has not been able to assess the study's methods.

"No causal relationship between this disease and aspirin has been scientifically proven," agrees Lewis Nolan, vice president for communications of Plough Inc., a manufacturer of children's aspirin.

But the industry has agreed voluntarily to put labels on aspirin products urging that a doctor be consulted before aspirin is given to a child with symptoms of flu or chicken pox. That step was taken because "there's public concern and there are many people who believe there is a relationship," White says.

Reye's syndrome develops in one of 100,000 American children under 18, usually within a week after chicken pox or flu. Symptoms include vomiting, breathing difficulties and neurological problems such as severe headaches, delirium, combativeness, hallucinations, disorientation and seizures. Without prompt treatment -- intensive care, intravenous fluids and medicines to control the pressure around the brain -- Reye's can progress to coma and, in about 10 percent of cases, cause death.

The massive federal study is being carried out by a task force of researchers from CDC, the Food and Drug Administration and the National Institutes of Health. It is expected to be completed by mid-1986 and is still on schedule, Barrett says, although finding suitable cases is becoming more and more difficult.

"We're doing everything we can to carry out the main study," he says. "That would be a very nice possibility -- not to be able to do the study because there wasn't enough disease."

The extent of the difficulty will depend partly on the severity of the impending flu season and its viral type, which won't be known until the first cases occur, probably in a few weeks.

Some types of influenza are more likely than others to develop into Reye's syndrome. In general, Barrett says, incidence of Reye's is higher in years when the dominant flu strain is type B, rather than type A, which predominated last year.