What happens when the antibodies in colostrum reach the infant's stomach? Why aren’t they destroyed by digestive enzymes?
There are two main differences between adults and newborn babies which allow the passage of antibodies (while maintaining the activity) through the stomach and the resorption in the gut.
The digestive activity of the stomach in newborns is still immature and needs to develop. This results in almost no production of hydrochloric acid (which is responsible for the very low pH in the stomach). It can take up to two years to until the pH in the stomach of children reaches the level of adults (see chapter 5 in reference 1). Because of this higher pH much more proteins (and other components of the milk like anti-microbial proteins, carbohydrates and lipids) can pass the stomach unaltered.
The other really important feature of newborns is their much greater permeability of their intestine. This allows an efficient transport from the antibodies into the blood stream and where they provide protection. See references 2 and 3 for more details.
Another important factor that the previous answer missed is that the antibody secreted in breastmilk is IgA dimer. IgA dimer is two IgA molecules linked by a protein called the secretory component, which protects the antibodies from being degraded in the digestive system.