There is a condition which is called 'harlequin icthyosis.' It is a horrible, horrible thing, and causes babies to die very soon after birth. Its not exactly a breathing disorder, but it is invariably fatal and quite swift. It doesn't matter if the baby is at a major hospital or not. Don't google it unless you want to see some disturbing pictures. Babies with this condition are horribly disfigured. If you are looking for shocks, look no further. Its something so unspeakably terrible that you never really hear about it.
SIDS is not so much a disease, but a result of babies not being able to breathe, usually as a result of being put to bed face down. This is why you see notices inside buses, maternity wards and doctor's offices telling mothers to always put their babies to sleep on their backs. (a SYNDROME is a collection of symptoms of indeterminate cause. a DISEASE is something that the cause is something known and specific)