At what age must I stop breastfeeding my healthy child. Am I allowed to go beyond 2 years of age. Can you point me to some Hadith or explanation as to why it is recommended to stop at two years?

There is no age where it becomes haraam to breastfeed the child, however it is recommended to stop at 2 years. If a child goes on further than 2 years it is allowed.
The verse in Quran says mothers suckle for 2 years