I don't know if this has been brought up, but are we sure William is even able to produce a child? I mean we assume that William and Mary's childlessness was because of her miscarriage, but could any of it be on William as well? I mean look at his mistress. Elizabeth Villiers was William III's mistress for almost 15 years, from 1680 to 1695, with no pregnancy whatsoever. Then, after she marries, she three children. So it seems to be that William could also be infertile or at the very least have low sperm count.