“There’s no question that this current rash of breakthrough cases is concerning, but the industry has not shut down,” said Charlotte St. Martin, the League’s president. “I’m knocking on wood so much I have bruised knuckles, but so far we’re still open, and a two- or three-day shutdown, now and then, I think is to be expected.”

Fans have been upset, frustrated, rattled, but also understanding.

“I’m not insane — of course they’re going to cancel a show if someone has Covid,” said Karleigh Kebartas, a 21-year-old psychology student at Pace University, who had a ticket to the canceled Saturday matinee of “Little Shop,” “but it’s disappointing.” Ms. Kebartas was already at the theater when the show was canceled — in fact, much of the audience was held in the lobby until several minutes after the scheduled start time, when an announcement was made with no explanation of the reason. But Ms. Kebartas got lucky — on Tuesday, she was able to buy another ticket to that night’s performance, enabling her to catch the show’s star, Jeremy Jordan, before heading home to Massachusetts for the holidays.

The closings began almost as soon as Broadway reopened. On Sept. 28, the Disney musical “Aladdin” resumed performances at the New Amsterdam Theater; the next day, the show canceled a performance, citing breakthrough cases, and then, after another performance, it detected more cases and took a 12-day pause.

Since that time, there have been a handful of closings at other shows — the lengthy shutdown at “Chicken Biscuits,” and shorter Covid-related shutdowns at “Chicago,” which went dark for a five-day stretch last month, and “Wicked,” which lost a weekend early this month. And it’s not just theater: The acclaimed Alvin Ailey American Dance Theater canceled its performances Wednesday and Thursday, citing positive coronavirus tests.

Plus there have been additional cancellations of “Harry Potter and the Cursed Child” and “American Utopia” that the producers said were not Covid-related.