Why do adult cells not divide as quickly or as frequently?
Rates of division vary from cell type to cell type. For example, skin cells at the top of the epidermis are replicating very often. Bone cells replicate through mitosis a bit slower. Think about the difference between a cut on your finger healing (mostly through cell replication) versus a bone breakage. Some cells once created never divide (nerve cells, red blood cells). The rate of division or frequency between divisions is controlled by the cell's DNA. Cancerous growths occur when this mechanism for controlling replication is disrupted.
I think your question may point toward the idea of embryonic stem cells versus differentiated adult cells. Embryonic stem cells are cells that can divide and become any type of cell in the body (nerve, connective, skin, muscle, etc.). There are also Adult stem cells that simplistically put are "cell factories" that make other cells. Examples of these can be found in a person's bone marrow, where all blood cells are created.
When a baby is growing and developing the DNA in those embryonic stem cells is giving instructions to divide more frequently than in an adult's. This is one of the reasons why stem cell research has great potential. The stem cells in embryos are able to differentiate into any type of cell, and the hope is that if Biologists can unlock the DNA's mechanism to turn on and off this growth process, we can stimulate adult cells to create new tissue.
~Mr. Angel ScienceGuy