This article is being republished as part of the articles that also appeared in the U.S. print edition of The Wall Street Journal (December 30, 2020).

Chef Matthew Kelly is one of the few restaurateurs who has fought property insurers over pandemic business restrictions and won.

His establishments are part of a group of restaurants that a North Carolina state court sided with this fall. The insurer has appealed the decision, which found the plaintiffs were entitled to payouts under business-interruption coverage.

“I’m excited that we’ve made it this far, but that excitement and the win does not translate into relief until the job is completed,” Mr. Kelly said.

Cases such as Mr. Kelly’s are keeping hope alive that some small businesses may receive insurance money to help them rebound from government-ordered shutdowns.

In hundreds of lawsuits across the country, mostly small businesses have sued their property-insurance companies for refusing to pay out “business interruption” claims tied to the pandemic. Many insurers say their policies contain clear language excluding virus-related claims, while most claims also haven’t met their policies’ criteria.

Many courts have backed up the insurers in their denials of payouts, but businesses are making progress. Of the roughly 100 rulings in suits pitting businesses against insurers, about three-quarters have been in favor of insurers, according to a Covid-19 litigation-tracking effort at the University of Pennsylvania Carey Law School.

Mr. Kelly, 44, was planning to open a fifth restaurant as the coronavirus hit. Instead, he shelved those plans and laid off about 100 employees. “It’s depressing,” he said, seated in his still-open Mateo Bar de Tapas in Durham. He pulled off a cap to reveal balding. “My hair is falling out” from the stress, he said.

Like many restaurant owners, Mr. Kelly said that he has taken on an enormous amount of debt — roughly $1.3 million in his instance — to keep eateries open. Two of his four restaurants are currently closed.

Among challenges for policyholders, business-interruption insurance coverage typically requires “direct physical loss or damage” to have caused the interruption. The insurers typically interpret this to mean tangible damage to property that requires repairs or rebuilding.

Business-interruption coverage is a subset of property insurance, and with few exceptions, insurers say they didn’t collect premiums for virus-related claims. Instead, most have included some sort of virus-specific exclusion since the SARS scare of the early 2000s.

The North Carolina ruling points to the types of complaints that may have the best chance of getting past industry defenses, lawyers say. The policies in the case, which were issued by units of Cincinnati Financial Corp. and covered a total of 16 restaurants, didn’t contain a specific virus exclusion.

Mr. Kelly’s lawyers focused on the absence of definitions in the policies for terms including “physical loss.” They also contended that prior North Carolina rulings don’t impose requirements for structural damage, as Cincinnati Financial and most other insurers contend.

In a September hearing, Mr. Kelly sat masked and socially distanced with the other restaurateurs as Judge Orlando Hudson said he would rule in favor of the policyholders. In his subsequent written opinion, the judge said the ordinary meaning of “direct physical loss” includes “the inability to utilize or possess something in the real, material or bodily world.”

In its filings, Cincinnati Financial argues that its policies don’t provide coverage for economic harm in the absence of “direct physical loss” to property, and it said such loss requires physical damage.

“We continue to believe that business-interruption coverage under our property policy in this case does not apply because there was no structural alteration to the property,” Cincinnati Financial spokeswoman Betsy Ertel said. “The prevailing view by courts around the country has been that an economic loss alone doesn’t qualify as direct physical damage or loss to property, which is the trigger for business interruption coverage.”

The restaurants’ financial losses are to be determined later, and could total $10 million across the 16 restaurants, said Gagan Gupta, one of the plaintiffs’ lawyers.

Nationwide, state and federal courts in recent weeks have picked up the pace in ruling on the more than 1,300 Covid-19 business-interruption coverage disputes filed since March, according to the University of Pennsylvania law school database. On Dec. 21 alone, at least four separate federal courts made rulings. Three granted insurers’ motions to dismiss and the fourth denied such a motion and allowed the policyholder’s case to move forward. Nearly 150 lawsuits have been voluntarily dropped, said Tom Baker, a Penn law school professor.

Some policyholders are having success by building off years-past rulings in which judges concluded that things like wildfire smoke, gasoline vapors and carbon monoxide created property damage for purposes of business-interruption coverage, lawyers said.

“It will come down to experts saying that, statistically, it is likely the virus was on the property,” said Robin Cohen, a principal with law firm McKool Smith.

In November, a judge in Clark County, Nev., denied an insurer’s motion to dismiss a case in which Ms. Cohen’s client, JGB Vegas Retail Lessee LLC, alleged that the coronavirus spreads through infected exhaled droplets “that attach to and cause harm to other objects.” The insurer has filed a motion for reconsideration.

Adam Moskowitz, a Florida class-action lawyer who represents numerous policyholders, said insurers “shouldn’t take comfort” from their initial run of success because some involved less-experienced lawyers who jumped in early with weak cases.

Insurers’ lawyers acknowledge tougher fights loom in cases that present unique circumstances, brought by law firms with deep insurance experience. But they remain confident the early successes will continue.

“We will litigate the legitimate disputes,” said Steven Badger of Zelle LLP, who represents insurers. “Those will be resolved like all insurance coverage disputes, through trial or settlement.”