Think in terms of billions of cells, not trillions...we're not THAT big.
There are a lot of things which affect cell reproduction, from the energy producing parts of the cell (mitochondria) to the hormonal regulation within the body which "tells" cells to stop reproducing or slow the process. As we age, hormone levels change, which plays a large factor in the cell reproduction level. As our glands age, they release less and less Growth Factor, which limits the rate of cell reproduction. We never STOP reproducing cells. Not until we leave this earth. Each of us produces hair cells, skin cells, and new tissue cells all the time. If we didn't, our cuts wouldn't heal and any scraped skin would never grow back. This, thankfully, doesn't happen.