Full question: Henry the 8th had syphilis, which is why Katherine of Aragon and Anne Boleyn had so many miscarriages, why didn't Mary Boleyn have the same problem? She slept with Henry about as much as the other two did but she also had four healthy children.
Historians today tend to discount the theory that Henry VIII had syphilis because there is no record of him being treated with mercury, the standard Tudor treatment for syphilis, or suffering with the illness. Also Henry did have three perfectly healthy legitimate children, as well as at least one (and probably more) healthy illegitimate child. So, I don't think that Henry had syphilis and that's why Mary Boleyn did not suffer any problems.
For information on the miscarriages and troubled pregnancies of Anne and Catherine, you can see http://www.theanneboleynfiles.com/the-pregnancies-of-anne-boleyn-and-catherine-of-aragon/4132/ - I think they were just unlucky women. Miscarriages are still quite common today and were even more so in those times, but one theory is that Anne was Rhesus Negative and therefore would not have been able to carry another child to term.