I'm a geneticist who works in clinical reproductive genetics. A reciprocal translocation involves 2 chromosomes swapping sections with each other. This makes it harder to produce genetically normal eggs or sperm, resulting in multiple losses up to congenitally abnormal stillbirths/early deaths (not so much nowadays obviously). Is it possible this is why Henry VIII had so much trouble with getting living children off of multiple women? Is there something I'm missing coming at it from a genetics nerd/BBC costume drama watching perspective?
I'm a little late, but I have some time on my hands and thought I'd answer this.
This is absolutely a possibility considered by historians. Perhaps the most popular theory to explain Henry's difficulty in having children is that Henry was positive for a blood group antigen known as Kell. 90% of Caucasian populations are negative, and a mismatch between partners usually causes antibodies to attack the foetal red blood cells, killing the foetus.
This would explain why Katherine of Aragon birthed 6 children, but only one (Princess Mary) survived. Katherine's sisters, Juana of Casile and Maria of Portugal, both easily produced living children, which would suggest Katherine and her siblings were Kell negative. If the issues with children were due to a genetic mismatch, this would mean the problem lay with Henry.
However, a number of other theories have been put forward to explain Henry's reproductive problems. Notably syphilis, though it is debated amongst medical historians whether this disease was actually present in Europe at the time, and this theory has been largely discredited due to no reports of syphilis in Henry's sexual partners.
However, we will never be certain unless Henry's remains are studied, and approval for this does not appear to be likely. But yes, the most popular theory is that Henry was positive for a K antigen.
Sources: