I wasn't aware that so many of the children from the Duke's first marriage suffered from poor mental and physical health. The second "wave" of children, by a different mother, appears to be a relatively healthy crop, however.
I'm speculating wildly here, with no hard facts to support this, but I wonder whether Princess Maria Grazia Pia might have had Rhesus-negative blood (e.g. blood type lacks certain proteins).
When a mother is Rh negative, and she gives birth to a child who is Rh positive (fairly likely, considering the vast majority of people have Rh positive blood), she begins to build up antibodies against future Rh-positive babies. The first baby is not affected because the antibody formation occurs mostly in the first few days after birth, in a response to the mixing of fetal and maternal blood at the time of the birth.
However, subsequent preganancies in an Rh negative mother may, in layman’s terms, result in stimulation of abnormal antibodies crossing the placenta, into the baby’s blood stream, triggering the destruction of the unborn child’s red blood cells. The second pregnancy often produces a mildly anemic and /or jaundiced infant, while succeeding pregnancies produce more seriously affected infants. In severe cases, newborn infants develop neurological syndromes which may, if they survive, lead to hearing loss, mental retardation, etc.
Rh incompatability went untreated until 1968, when an Rh immunoglobulin shot (which contains preformed antibodies and basically “resets” the mother’s body prior to the time when her body developed the antibodies) was developed. Since then, Rh incompatability is no longer a threat to either mother or child.
I'm guessing that may have been the case here. The pattern certainly fits. I am thankful for modern medicine myself.