ANSWER: The question of what the Bible says about birth defects and why they are allowed to exist is a tough one to handle, especially for parents who have children with disabilities. I come from a family that has a history of genetic-related problems (e.g. ADD, ADHD and others) and struggle with such birth defects on a daily basis.
I have friends who suffer trials brought by manic depression, Asperger's syndrome and others, and sadly have known a few folks who have committed suicide. Struggling with genetic defects, manifested at birth, is something that is seen and experienced each day.
Birth defects occur because of sin, but this is not the complete answer. God has chosen to allow sin and its consequences for a very special purpose. His great plan is for make man fully into his own image (Genesis 1:26). In order to reach his goal he has given us creativity and the ability to choose right from wrong. He also allows the effects of our poor choices, and the fact that humanity in general is cut off from him, to bring its consequences upon countless others.
Defects that exist at birth are the result of poor choices by others and genetic mutations passed on to those who are otherwise innocent.
For example, if a mother takes illegal drugs during her pregnancy there is a much higher risk she will give birth to a baby will be born with disabilities. If a mother smokes or drinks too much alcohol prior to or during the time she is pregnant she can pass on a whole host of problems to her unborn child. Even if a person's parents were healthy when they were conceived, they can still be the recipient of genetic defects that exist in family lines.
The Bible does give us a fascinating example of an innocent person knowingly allowed to suffer, from the time he was born, the consequences of a genetic abnormality. Jesus' healing of a man who came into this world blind is a striking and prime example of how God accomplishes his goals through human weakness and frailty.
One day, while Christ was walking with his disciples, he saw a man who was blind from birth (John 9:1). The disciples, who assumed diseases and afflictions came as a punishment from God, asked whose sins caused the man's blindness. Jesus' swift answer was that neither the man, or his parents, had sinned nor caused the physical birth defects he experienced (verse 3).
During Jesus' day (and for most of human history), being born with such a disability virtually guaranteed a life of suffering, poverty and rejection. The man was allowed to be blind, however, so that his healing would be a powerful testimony of the Father's mighty power and a witness that the Lord was indeed the Savior of mankind.
In Ephesians 3:15 the apostle Paul states that God is building a family. His purpose is to have humanity become His spiritual sons and daughters where Jesus is the firstborn (Romans 8:29, Colossians 1:18). Those who suffer from birth defects can be assured that they have done nothing wrong to deserve all the trials, troubles and struggles that have come their way because of it.
In reality, we all have disabilities of one kind or another. We all struggle with a variety of problems and challenges made worse by our human nature given to us at birth. All our problems are allowed so that we learn to reject Satan's way of life and accept what the Lord has to offer.
Many times, those who suffer defects from birth draw closer to God and His ways, during their lives, than others who seem to have fewer problems. We also need to keep praying to ask for the help we need to deal with our disabilities and keeping reading the Bible to understand His will. He will answer us in such a way that will bring glory to him.