The weekend meltdown encapsulates challenges that several U.S. airlines—and Southwest in particular—have grappled with all summer, as travel came roaring back faster than carriers anticipated.

Spirit Airlines Inc.

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canceled 2,826 flights over a 10-day period in August—some days scrubbing over 60% of its flights—during a similar cascade of bad weather, technological system outages and staffing shortages.

American Airlines Group Inc.

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trimmed back its schedule in July after a series of storms in June created strains. But while other airlines have managed to bring operations under control, Southwest has been caught in a spiral of planning missteps and labor tensions.

Southwest believed it was ready to handle heavier traffic for the Columbus Day holiday weekend, but the airline said a confluence of unexpected events threw it off course.

The trigger came Friday when severe weather in Florida and air-traffic control issues, including ground-delay programs, resulted in a large number of cancellations. Close to half of Southwest’s planes fly through Florida on any given day, so disruptions there can ripple out to the rest of the country, said Mike Van de Ven, the airline’s president and chief operating officer.

By the end Friday, hundreds of planes and crew members weren’t where they were supposed to be, setting off a chain reaction that has taken days to sort out, Mr. Van de Ven said. Pilots and flight attendants bumped up against limits to how long they can work, so the airline had to pull flight crew from reserves. With thousands of trips on the books without a full complement of crew, the airline had to cancel flights and ferry aircraft to try to reset itself.

“It took us Saturday and Sunday to really get the network stabilized,” Mr. Van de Ven said in an interview. “Hopefully we’ll be completely back to normal by Wednesday morning.”

The episode has been a frustrating re-emergence of a predicament the airline’s leadership believed it had managed. In June, a series of technical problems snarled Southwest’s operations for days, prompting hundreds of cancellations. About one-third of the airline’s flights were late over the summer, compared with about 21% in 2019, according to Cirium, an airline-data provider. Southwest executives have apologized to passengers and employees, pledging to run a more reliable operation.

Southwest’s shares fell 4.2% to $51.67 on Monday.

One major problem this summer has been staffing, airline executives said. Carriers received $54 billion in federal aid to continue paying workers throughout the pandemic but with the outlook uncertain also encouraged thousands to retire early or take long-term leaves of absence.

Southwest had about 5,000 employees leave permanently and 11,000 go on extended leaves. Once demand shifted, the airline struggled to call them back and retrain them quickly enough, Southwest executives have said.

At the same time, Southwest flew an ambitious schedule in an effort to capture the rising demand. The airline seized what its leaders saw as an opportunity during the pandemic to extend its reach, announcing plans to launch service to 18 new destinations to tap into new markets in search of revenue. But the plan also left its resources stretched thinner. With fewer flights between pairs of cities and packed planes, executives have said it has been harder to bounce back from storms or technical problems.

The airline’s staffing models rely on assumptions about how many pilots will pick up open trips, how many will be sick or on medical leave or in training. This year, Covid-19 illness and quarantines have also factored in. During much of the summer, Southwest offered increased overtime pay in an effort to prevent staffing crunches.

“It’s clear to me that we were too aggressive going into the summer with those assumptions,” Mr. Van de Ven said.

The airline had cut planned flying this fall in an effort to ease the strain and catch up on hiring and had built up a larger reserve of crew who were on call to assist this month. In recent weeks, about 80% of Southwest’s flights were on-time—a sign of improvement, Mr. Van de Ven told employees in a message Sunday.

But Southwest was also planning more flights Sunday than any day since April 13, 2020, according to Cirium data, leaving the airline without much of a cushion.

The snarls this summer have contributed to tensions between Southwest and the union that represents its pilots. The union said the weekend’s problems were a sign that pilots’ concerns that have been raised for months have yet to be addressed.

“What was a minor temporary event for other carriers devastated Southwest because our operation has become brittle and subject to massive failures under the slightest pressure,”

Capt. Casey Murray,

president of the Southwest Airlines Pilots Association, wrote in a message to members Sunday night.

Mr. Van de Ven said that in hindsight, the airline perhaps should have made deeper cuts to its flight plans this month, and Southwest is now looking at whether it should throttle back flying again in November and December. Expanding into new cities was the right decision, he said, but the airline is rethinking how it plans and balances the trade-off between generating revenue and running a reliable operation. Southwest will have to have higher staffing levels than it might have otherwise, for example.

“We want to make sure that we offer a reliable product to our customers and certainly to our employees, and that it has enough cushion in there, enough resiliency in there, that when we have these kinds of shocks that we can perform better than we did,” he said.

Southwest and the union that represents the airline’s pilots pushed back on suggestions that pilots were calling in sick in protest of Southwest’s plans, announced last week, to require employees be vaccinated. The airline has said it must require vaccination by Dec. 8 to comply with new federal rules for government contractors.

“The weekend challenges were not a result of Employee demonstrations, as some have reported,” the company said in a statement.

The union’s Mr. Murray said in an interview that sick calls are in line with summer levels and that pilots are offering to work unassigned trips at high rates.

Write to Alison Sider at alison.sider@wsj.com