"The standards for promotion of today's flag and general officers have never been higher, but the failure to promote does not diminish the achievements of a lifetime of service," Rear Adm. Dawn Cutler, head of the Navy's Office of Information, told Navy Times in a statement.
Losey plans to retire, she added, after he passes command onto Rear Adm. Timothy Szymanski, though a date has not been set.
"While the full scope of his service may never be known, his brilliant leadership of special operators in the world's most challenging operational environments, including multiple combat tours, reflected his incredible talent, energy and devotion to mission," Cutler said.
A 33-year veteran, Losey has commanded Naval Special Warfare since 2013.
Meghann Myers is the Pentagon bureau chief at Military Times. She covers operations, policy, personnel, leadership and other issues affecting service members.