Less than four months ago, start-up airline OneJet announced it was buying a charter operator to more than double its flights to 400 a week. This week, OneJet suspended all operations.

The operator of Pittsburgh International Airport this month sued the three-year-old company, which has a base at the airport, alleging OneJet did not fulfill the requirements for a $1 million incentive it gave the airline to expand its operations. Rick Pawlak, managing director of Ultimate AirShuttle, a unit of Ultimate JetCharters, a charter company based at the Akron-Canton Airport in Ohio, told CNBC it terminated its acquisition agreement with OneJet and it has stopped flying for the upstart.

CEO Matthew Maguire founded OneJet in 2015, going after business travelers for companies such as FedEx in midsize cities that large carriers retreated from in a wave of megamergers over the last decade.

The turmoil highlights the difficulty and complexity of operating and expanding an airline, particularly as rising costs for even the world's largest airlines are taking a bite out of profits. Four carriers control some three-quarters of the U.S. market, and corporate travelers tend to fly on large airlines since they offer many more flights and business-class travelers' plans often change.