The chance of having a child with Down's Syndrome does not only have to do with cell division, but the mechanism that allows spontaneous abortion to occur within the uterus of the mother.
There is strong evidence for uterine selection against genetically disadvantaged embryos. However, as women approach the menopause and the risk of future infertility increases, this selection, or filtering stringency, is expected to relax.
Neuhäuser and Krackow’s paper provides evidence that older mothers, who give birth to children with Down Syndrome, have a relaxed stringency of quality control of embryos (or relaxed filtering stringency), which increases the probability that these women will bring children with developmental defects to full term. They believe that this relaxed filtering stringency is an adaptive maternal response and it might explain why the rate of Down Syndrome accelerates with increasing maternal age.
Basically, the mechanism that allows for the uterus to select against 'genetically disadvantaged embryos' (which can be Down's Syndrome, or other genetic deficiencies) is not as good at detecting these problems, OR as this paper suggests, is 'less picky' about the genetic quality of the fertilized egg, and will allow it to implant in the uterine walls.
It is also important to note that these studies are all ongoing, and many different reasons for the development of Down's Syndrome are unknown.
Neuhäuser M & Krackow S (2006). Adaptive-filtering of trisomy 21: risk of Down Syndrome depends on family size and age of previous child. (Naturwissenschaften, DOI 10.1007/s00114-006-0165-3)