Is there a time at which it becomes unhealthy to breast feed by child?

No. The physical benefits , such as increased immunity, seem to max between 6-12 months. The emotional issues of prolonged breast feeding in our environment is what is not clear.
Open to Opinion. Breast feeding is both nutrition & nurturing & infants need both.Many aboriginal cultures breast feed until 2yr and place on solids as their norm.These kids thrive as well as any. Within our culture, most are supportive until baby is able to sit at the table. I believe some babies need extended nurturing& if so that is ok. If baby is ready to quit but mom is not, there is a problem.