Why can a child, who has previously been immunized against whooping cough, develop signs of the disease?
Possibly, that when the child was immunized, his/her body was not ready to produce antibodies yet.
It is important to remember that infants have an underdeveloped immune system, and our B lymphocytes are part of this statement.
It may be possible that when the vaccine was injected, there was no immune response due to the underdeveloped immune system that the child has.
It also may be possible that the child has an acquired immunodeficiency.
Hope this helped! :)