Spirit Airlines Inc. on Wednesday canceled hundreds more flights but said it is working to reset operations.

The low-cost airline canceled 60% of its flights Wednesday for the second day in a row, according to FlightAware. Spirit has been grappling with what it has described as “overlapping operational challenges” since Sunday, including bad weather, technology-system outages and staffing shortages.

Spirit said Wednesday that the airline was rebooting its network to help speed the process of reassigning crews and restoring flights. A spokesman said the airline expects the number of canceled flights to begin to fall Thursday and in the coming days.

“The last three days were extremely difficult for our Guests and Team Members, and for that we sincerely apologize,” the airline said in a statement. The airline said it had planned to learn from the problems and had identified ways to improve.

For Spirit, the last few days have been a major setback in the budget carrier’s effort to improve performance and win passengers’ loyalty.

Jon Enrique Torres, who was due to fly home to Austin, Texas, on Spirit Saturday after visiting friends and family in Puerto Rico, missed his flight while waiting in a long line he said was full of passengers from another Spirit flight that had been canceled.

Spirit rebooked him on a flight that was supposed to depart Tuesday, but that flight was canceled, he said. Mr. Torres said he has been promised a refund and now plans to depart Thursday on a JetBlue Airways Corp. flight.

“I would never trust this airline with anything again,” he said of Spirit.

The Association of Flight Attendants-CWA, the union that represents Spirit’s flight attendants, said it met with the airline’s management Tuesday to discuss the problems. The union said it has negotiated measures including premium pay to encourage flight attendants to pick up extra flying and new security measures to protect crew amid a tense environment in some airports in recent days.

“In an operational breakdown like this, the airline needs to ’reset’ in order to recover quicker and prevent further disruptions that could last weeks,” a union spokeswoman said. “The reset will see significant cancellations in the short term but avoid long term disruptions.”

American Airlines Group Inc., which also canceled hundreds of flights this week after severe storms hit its Dallas-Fort Worth hub Sunday, had about 118 cancellations Wednesday, significantly fewer than in recent days, according to FlightAware.

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