Cognitive Daily has an elegant summary of research on why we don’t remember the first years of life. The results suggest that it may be because young children lack the language resources to support the necessary memories.
I would be tempted to quote some of the post here, but its described so succinctly its probably best just to read the original.
Link to ‘Why do we forget our childhood?’ from Cognitive Daily.
Mind Hacks 
There are many kinds of memories. In infancy the cognitve mind has not yet developed however the affective mind is very much aware. We are able to create implicit affective memories right after birth if the event creats enough affect. For example suppose a mother died a few days ow weeks after birth. The infant would be aware that the mother suddenly vanished and would not accept any woman as a substitute. We have research that shows infants taken from their mothers experience grief shock and repression. (Robertson and Bowlby 1952).We also have eveidence that many adopted infants feel intense grief throughout their lives for their bonded birth mothers even when raised in a loving family.