Spirit Airlines Inc. canceled over half its flights Tuesday as the airline continues to grapple with an operational meltdown that has thrown its operation into disarray for three consecutive days.

Spirit canceled 373 flights, or 54% of its schedule Tuesday, after canceling over 40% of its flights Monday and close to 20% on Sunday, according to FlightAware, a flight-tracking site.

A Spirit spokesman cited “overlapping operational challenges” including bad weather, system outages and staffing shortages in some areas. He said the airline had proactively canceled some flights in an effort to reset its operation and was working to refund and rebook customers.

The Association of Flight Attendants-CWA, a union that represents flight attendants at Spirit and other airlines, said the struggles were compounded by an IT outage Tuesday morning that prevented crew schedulers from being able to access their system for over an hour. Spirit didn’t immediately respond to a request for comment on that outage.

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This summer has been difficult for airlines and passengers. Travel has surged, with the number of passengers hitting a fresh high Sunday since the start of the pandemic, but airlines and airports don’t have as much staff as they used to and have in some cases struggled to keep up and to recover when things go awry.

Bad weather, which isn’t uncommon in the summer months, has exacerbated the strains. Unlike snowstorms and hurricanes that airlines can prepare for in advance, thunderstorms are unpredictable. They can lead to major disruptions that take days for airlines to untangle. Airlines are still operating reduced schedules, and with fewer, fuller flights it has been difficult for them to rebook passengers whose plans are upended.

Spirit, the South Florida-based budget carrier, known for its no-frills service, has worked to revamp its image in recent years after chronic delays and cancellations sullied its reputation with passengers and became costly.

But analysts say that elements of Spirit’s business model make it harder for the airline to bounce back when things go wrong. It doesn’t always offer multiple flights on every route each day, so passengers can get stranded for days if a flight is canceled. And the airline doesn’t have deals to place passengers on competitors’ flights in the event of disruptions, an industry practice known as interlining.

American Airlines Group Inc. also canceled hundreds of flights this week following a prolonged bout of severe weather that began Sunday night at its Dallas-Fort Worth hub and continued into Monday morning. As of Tuesday afternoon, American had canceled about 9% of its flights, but the number appeared to be stabilizing throughout the day.

The nine-hour weather event resulted in delays and cancellations as well as over 100 diverted flights. Diversions can result in cascading problems as airplanes end up in the wrong cities and flight crews bump up against federal limits on how much they can fly in a day before they have to be replaced.

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