Yes, women with Down Syndrome are able to reproduce. They can get married and have babies just like anyone else. However, some challenges with people with Down Syndrome is that they may have other medical issues that sometimes go along with Down Syndrome. For instance, they may also have issues with congenital heart failure or issues. This sometimes among other problems may cause a problem with having children.
Anyone who has heart problems or other medical issues will probably have trouble giving birth. That is not to say that women with Down Syndrome can’t reproduce because they surely can. Like most parents, they should use the resources out there to help them take care of their children when they give birth.