When the National Park Service doesn’t want it to be.
Congress designated the David Berger Memorial as a national park unit in a 1980 national parks bill. As is its custom, Congress included a statement of national significance and assigned authority over the memorial to the Department of the Interior, of which the National Park Service is a part. As is also congressional custom, it did not provide funds for what it had authorized.
The memorial makes up the entire David Berger National Monument. It remembers David Berger, a weightlifter with dual US-Israel citizenship who was one of the eleven Israeli athletes killed by Palestinian terrorists at the 1972 Munich Olympics. Eight Cleveland families, all friends of Berger’s parents, commissioned and paid for the sculpture.
Berger’s parents, Dr. Benjamin and Dorothy Berger, were long-time friends of Howard Metzenbaum, who represented Ohio in the U.S. Senate from 1976 to 1995. That’s presumably how the monument ended up getting designated as a national memorial.
Is it a national park unit? You can argue it either way. The National Park Service doesn’t have it on the official list of park units but it’s on several official websites and brochures. The unofficial word is that NPS staff have never thought it “worthy.”