For some cultures, there has been an employment category called "wet nurses" whose entire job was to look after an infant and breastfeed it as a mother would. Perhaps as society becomes more an more unequal, we'll see a resurgence of wet nurses for rich infants.
Anecdata tells me that women who are stressed out won't produce much milk, so... I assume that's a significant number of people right there.
EDIT: Changed phrasing per reply
The article describes a market where companies pay women for breast milk that is left over after they have fed their own babies, and use it to produce a pharmaceutical product for premature babies. The controversy is between non-profits and for profit companies both doing this (but the non-profit doesn't pay the women).
It's actually not that uncommon and in most cases these women are otherwise perfectly healthy and really want to breast feed.
Many non-physiological factors play a role here. For example how much pressure does the mother feel or put on herself. (typically with the first child because it's a new experience) How much stress does she have and so on.
We had to bottle feed her, and eventually the pumping wasn't enough to continue the supply, or allow the supply to fully "come in".
Later age is correlated with lower milk production, kicking up the demand http://www.reuters.com/article/2010/07/27/us-milk-production...
I'd say now with my second baby, at 11 months, 90% of the bedtime and morning nursings are pleasant bonding experiences, and half of the daytime ones.