A New Jersey couple who gave their children Nazi-inspired names should not regain custody of them, a state appeals court ruled Thursday, citing the parents' own disabilities and the risk of serious injury to their children.

The state removed Heath and Deborah Campbell's three small children from their home in January 2009.

A month earlier, the family drew attention when a supermarket refused to decorate a birthday cake for their son, Adolf Hitler Campbell. He and siblings JoyceLynn Aryan Nation Campbell and Honszlynn Hinler Jeannie Campbell have been in foster care.

A family court had earlier determined that there was insufficient evidence that the parents had abused or neglected the children. That decision was stayed until the appeals court could review it. On Thursday, the three-judge appeals panel determined there was enough evidence and that the children should not be returned.