Once the gene has been edited, things will work. But at some point that cell will die. Why would the replacement cell also have the edit? The DNA in the rest of the body's cells will still not be correct.
When cells duplicate they have the same (altered) DNA so the mutated cells survive.
You'll end up with mosaicism (cells with different DNA) but presumably you have enough of the new cells to fix the problem the original ones had.
You don't need to fix all the body, you just need to fix some of the, say, liver, and you're good.