Southwest Airlines was responsible for the majority of cancelations during and after a winter storm (Picture: Getty Images)

Southwest Airlines’ meltdown following a winter storm has continued with thousands of additional cancelations and failures to rebook and refund – all under investigation by the US government.

On Wednesday, the Dallas-based airline canceled 2,500 more flights, or 61% of its service schedule, according to FlightAware. That was after calling off more than 60% of its flights on Tuesday and disrupting over 80% of its flight schedule on Monday.

There is no relief confirmed on the way yet. The company has canceled more than 2,300 flights on Thursday and said it may be days out before getting back to normal service.

Southwest has failed to rebook most flights and many customers have not managed to obtain refunds. Thousands of travelers remain stranded at airports and some have been separated from their suitcases that flew without them and are piled up at baggage claims.

Unclaimed luggage piles up at baggage carousels during the Christmas holiday weekend at Orlando International Airport (Picture: Getty Images)

US Transportation Secretary Pete Buttigieg on Wednesday said that ‘meltdown’ is ‘the only word I can think of to describe what’s happening at Southwest Airlines’.

‘We are past the point where they could say that this is a weather-driven issue,’ Buttigieg said.

‘What this indicates is a system failure, and they need to make sure that these stranded passengers get to where they need to go and that they are provided adequate compensation.’

The federal government has said it will investigate the lag. The Senate commerce committee also vowed to begin a probe, with two Democrats saying Southwest has money and should provide ‘significant’ compensation to customers because it plans to pay $428million in dividends in January.

The holiday travel period has been plagued by a winter storm and thousands of delayed and cancelled flights, mostly by Southwest Airlines (Picture: Getty Images)

Southwest CEO Bob Jordan apologized to customers and admitted that staffing issues were a ‘giant puzzle’ that could persist for days.

‘Our plan for the next few days is to fly a reduced schedule and reposition our people and planes,’ said Jordan. ‘We’re making headway, and we’re optimistic to be back on track before next week.’

Southwest Chief Operating Officer Andrew Watterson told employees in a call on Tuesday that outdated scheduling software was the main cause of service disruptions after the storm, CNN reported.

While many airlines return their planes to their hubs, Southwest uses a different ‘point to point’ system.

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The federal government will investigate why Southwest Airlines lagged behind other carriers after a winter storm.