SIDS

Sudden infant death syndrome or SIDS is a diagnosis used to describe the death of a person under the age of twelve months by oxygen starvation without any evidence of suffocation, respiratory distress or trauma. It usually occurs during sleep and between the hours of midnight and 9 a.m. It accounts for roughly 80% of deaths of otherwise healthy infants. It is largely a diagnosis of exclusion. About 19,000 deaths a year are diagnosed worldwide. 
The underlying cause of such deaths is not well understood, but the following factors appear to increase the risk:
* Family history of such deaths
* Age between 2 and 4 months
* Environmental stress, particularly cigarette smoke
* Premature birth
* Sleeping on the side, rather than the back
Sudden infant death syndrome at Wikipedia