The case is being argued by Enrique Vila, lawyer for SOS Ninos Robados or SOS Stolen Children, a Spanish advocacy group, ThinkSpain reported Wednesday.
The family says the baby was reported to be stillborn by the Malaga Civil Hospital in 1964, but neither the mother nor any of her relatives saw the body. They also said the hospital has no records showing the baby was buried.
Spain's highest court, the Constitutional Tribunal, dismissed the case on the grounds that the family waited too long to take legal action.
Vila and other advocates say thousands of children were falsely reported as stillborn between 1960 and 1990 and given to other families.
Carlos Ferreiros, prosecutor for the children's court in Alicante, said no stolen baby case has yet been proved. He said that the bodies of 15 infants reportedly stolen have been exhumed and all that have been positively identified matched the records.