The board of DSA is reviewing options for the site following lengthy deliberations which "reluctantly concluded that aviation activity on the site may no longer be commercially viable."
Owners Peel Group said they had taken external independent advice and concurred with the board's findings on the airport, which opened in 2005.
The news comes after managing director Chris Harcombe stood down from his role as managing director earlier this year.
A statement from Peel L&P said despite significant investment and growth in passenger numbers DSA had "never achieved the critical mass required to become profitable."
It said the shortfall was exacerbated by the announcement in June of Wizz Air's withdrawal from the airport leaving only one base carrier, TUI.
It added: "This challenge has been increased by other changes in the aviation market, the well-publicised impact of the COVID-19 pandemic and increasingly important environmental considerations. It has therefore been concluded that aviation activity may no longer be the use for the site which delivers the maximum economic and environmental benefit to the region."
Robert Hough, Chairman of Peel Airports Group, said: “It is a critical time for aviation globally. Despite pandemic related travel restrictions slowly drawing to a close, we are still facing ongoing obstacles and dynamic long-term threats to the future of the aviation industry.
"The actions by Wizz to sacrifice its base at Doncaster to shore up its business opportunities at other bases in the South of England are a significant blow for the airport."