Down's syndrome occurs when either the egg or the sperm cell contain on extra chromosome 21. To my understanding, women are born with all the egg cells in place already, so there's no further cell divisions, and thus no further chance of having one cell with an extra chromosome.
Now, the chance of having a baby with Down's syndrome increase with age:
At maternal age 20 to 24, the probability is one in 1562; at age 35 to 39 the probability is one in 214, and above age 45 the probability is one in 19
Why is this so, when the egg cells are complete at birth?