Businesses, however, continue to litigate in hopes of a payout.

“What has happened to the policyholders throughout the nation has been fundamentally unfair,” said

Robin Cohen,

chair of the law firm Cohen Ziffer Frenchman & McKenna. She aims to convince New York’s highest court that insurance companies have tried to get out of what they owe her client, Consolidated Restaurant Operations Inc., which runs dozens of restaurants and employs more than 3,200 people.

“They took in these premiums and they assumed the risk,” she said of the insurers. “If they assumed incorrectly, the mom-and-pop restaurants shouldn’t be penalized.”

Federal appeals courts so far have rejected cases like Consolidated Restaurant’s. On Tuesday, the Second U.S. Circuit Court of Appeals in New York threw out an appeal from

ITT Inc.,

a diversified manufacturer based in Stamford, Conn. That decision followed a 2021 ruling by the same court against a Manhattan art gallery.

In January, the federal appeals court in Philadelphia ruled against a range of businesses. With that decision, businesses had seen losses in 11 federal appeals courts, whose jurisdictions span nearly the entire country.

Business interruption insurance policies are typically written to address harm to property: For instance, if a water-main break floods a sales floor, or a fire forces a business to close. But many courts have said Covid-19 isn’t the same.

In June, a Boston federal appeals court rejected a Covid insurance claim by a group of restaurants. “Evanescent presence of a harmful airborne substance that will quickly dissipate on its own, or surface-level contamination that can be removed by simple cleaning, does not physically alter or affect property,” the court said.

But courts have long recognized that some similarly fleeting events—an invisible ammonia leak, for example—can trigger a payout from business interruption insurance, said

Scott Godes,

a partner at law firm Barnes & Thornburg LLP. His firm is also representing clients suing for Covid-related losses.

Many policies explicitly exclude coverage for viruses. After the 2003 outbreak of SARS caused massive losses to insurers, many protected themselves going forward by writing viruses out of their policies, according to the National Association of Insurance Commissioners, a standards-setting organization. Big payouts, such as a $16 million business interruption claim paid to the Mandarin Oriental Hotel Group International Ltd., led many insurers to tighten policy language. 

But not all policies exclude losses from viruses. Despite setbacks for some policyholders in federal court, the cases that are still live could lead to large payouts if the courts find in their favor—the restaurant operator represented by Ms. Cohen has a $50 million policy with no virus exclusion, for example, according to a legal brief.

Even so, policyholders are unlikely to win any definitive victory through a single court decision. The insurance industry is regulated at the state level, which allows dozens of state and federal courts to weigh in and come to different conclusions.

“There are a lot of moving parts,” said Mr. Godes. “There can be standardized language sold around the country, and yet you could have dozens of decisions, if not more, with differing results and differing analyses.”

The American Property Casualty Insurance Association, a trade group, said it was pleased with the decisions and continues to hold that business interruption policies weren’t meant to cover diseases.

Laura Foggan,

a lawyer at Crowell & Moring LLP who has represented the association in some cases, said the federal appeals courts had resoundingly weighed in on the side of insurance companies.

“To have this many decisions that have reached the same conclusion is such a solid wall of authority,” she said.

Some insurers are already planning for the next pandemic. Brokerage Marsh LLC has partnered with insurer Munich Re to offer a product, PathogenRX, that can be triggered by “outbreaks, epidemics and pandemics.” That insurance, though, is meant for midsize to large businesses, and its pricing is bespoke, a Marsh spokeswoman said.

Many experts believe that private insurance alone can’t take on pandemic-related risks, because such threats are “systemic, correlated and non-diversifiable,” according to a survey by the standard-setting body NAIC. That is, pandemics by definition happen everywhere, all at once.

RIMS, a society of risk professionals, has pushed for Congress to pass a law that would make the federal government a financial backstop for insurers that offer pandemic-related coverage in the future.

The proposed legislation, however, doesn’t have a lawmaker on board to champion it, said

Lynn Haley Pilarski,

the chair of the group’s public policy committee.

“There’s a lot of Covid burnout,” she said.

Write to Richard Vanderford at Richard.Vanderford@wsj.com