Heath Campbell told The Associated Press last year that he believed the children were taken because officials felt they were in "imminent danger." He accused the state of removing the children because of their names and said government officials were relying on unproven accusations made by a neighbor and by an ex-wife who charged him with abusing her years ago.
The children's names and the birthday cake were not mentioned in Thursday's ruling. The court found that there were myriad other reasons that proved the need for continued protection services for the children.
According to court records, both parents are unemployed and both suffer from unspecified physical and psychological disabilities.
The court found that both parents were themselves victims of childhood abuse and said neither "have received adequate treatment for their serious psychological conditions."
Heath Campbell, 37, cannot read and Deborah Campbell dropped out of high school before finishing the 10th grade, according to court records.
In its ruling, the panel found the parents "recklessly created a risk of serious injury to their children by failing to protect the children from harm and failing to acknowledge and treat their disabilities."
The judges considered a typo-riddled note signed by Deborah Campbell and given to a neighbor. In it, Campbell says that if she were found dead, her husband was to blame.
"Hes thrend to have me killed or kill me himself hes alread tried it a few times. Im afread that he might hurt my children if they are keeped in his care. He teaches my son how to kill someone at the age of 3," the letter read in part.