Most women don't begin their nursing relationship with their infant with the idea of nursing for a set number of months. My toddler's anxieties and bumps and bruises are so easily soothed by nursing. Putting him or her to bed is a breeze, and grumpy mornings just don't happen when he or she wakes with a nurse. Toddlers can also be taught polite ways to ask for nursing. A hand gesture can be a secret way to ask to nurse rather than pulling on a shirt for the preverbal toddler.
Some moms are also comfortable establishing a no nursing in public policy.
And of course, some moms find that there is no reason not to nurse an older child in public. Of course they do, they have needs for privacy and needs for social time away from their family just like any mother, independent of whether they are nursing or not. The breast is an amazing organ, and as the months go by, breasts are less and less prone to problems such as engorgement, plugged ducts, or mastitis at time apart from nursing. That depends on your toddler and you. Many will self wean if you direct a weaning strategy of not nursing except upon request.