CNN  — 

A German family that claims it will be persecuted for homeschooling if sent back, lost its asylum request Monday at the U.S. Supreme Court and could be deported.

The justices, without comment, turned down the appeal of Uwe and Hannelore Romeike, who applied to stay in the United States on grounds of religious freedom.

Keeping with their Christian beliefs, they are educating their five children at home.

They said German law requires all children to attend public or state-approved private schools, and that such institutions “engendered a negative attitude toward family and parents and would tend to turn their children against Christian values.”

The Romeikes claimed German authorities threatened to take custody of their children if they did not comply.

The family moved to east Tennessee six years ago and applied for asylum with the U.S. Citizenship and Immigration Services.

An immigration judge initially granted their request in 2010 to the Romeikes and their children, saying they were “members of a particular social group” and would be punished for their religious beliefs if returned.

But the Justice Department revoked it last year.

The Board of Immigration Appeals concluded homeschoolers are too ‘amorphous” to constitute a social group eligible for protection under the asylum law.

“It was the last judicial hope for the family, but we will not give up,” Michael Farris, the Romeike’s lawyer, and chairman of the Virginia-based Home School Legal Defense Association.

“Although our judicial efforts on behalf of this courageous family are over for now, we are resolved to fight on for them and homeschooling freedom,” Farris said in a written statement.

More than 127,250 people have so far signed an online White House petition requesting President Barack Obama grant the Romeikes asylum.

The high court appeal was their last realistic chance to remain in the United States and the justices’ refusal to intervene means removal proceedings by the federal government can resume.

The case is Romeike v. Holder (13-471).