"What was "so common" which would explain why there was no word to describe a parent who had lost a child?"

I interpreted the statement as meaning that "infant mortality" was "so common" that almost all parents fell into the category of "parents who had lost a child", and that there was therefore no need to differentiate among parents by coining a special word which would essentially apply to the majority of them. I'm not sure enough of the statistical basis for this statement (i.e., what percentage of parents suffered child loss during the "period of the development of the English language"), but the premise doesn't seem that far fetched to me.