Yes, the death of a child can cause PTSD (post traumatic stress disorder). The unexpected death of a loved one is one of the most common causes of PTSD. And when that loved one is a child, it can also lead to depression, and even suicide. If you poll people who have children, many will say they would not know how to go on living if that was their child that died.
Thus, it is important for family, friends, and mental health professionals to support and reach out to those who have lost a child. Nothing is more devastating than the loss of a child.