Syphilis or congenital defects?

I was watching the Martin Freeman episode of Who Do You Think You Are UK recently. His great grandfather's third wife bore him 12 children, six of whom died in infancy. It turned out that most likely this high rate of infant mortality was due to syphilis. There were one or two children who were healthy, then six who died, then the remaining ones survived childhood. The sexual health expert interviewed for the program said that the most common reason for a block of children in one family to not survive was syphilis. Apparently after infection, over a period of four to six years, the first pregnancies would have resulted in miscarriage, the next few would likely have been stillborn, the next few would have failed to thrive (and lived or not), and then the next children would be healthy, after the syphilis infection had run its course. He also said that 100 years ago, the rate of infection with syphilis in the population was about 1 in 10, so therefore, most family historians were likely to find cases of syphilis somewhere in their ancestry. Today, syphilis is treated with antibiotics, so is no longer the large social problem that it once was.

I thought about families in my ancestry who might fit the bill, and the one that leaped out at me was the family produced by William Rich's first marriage. Of the nine known children, none survived childhood. Of course, there is the complicating factor in this case that William married his first cousin, and so therefore there could well have been congenital causes for many of the deaths. But I think it is worth considering that syphilis was a possibility as well, so I have put together all the relevant information I have:

Name	Date of birth, place	Date of death, place	Age at death	Listed cause of death
William H Rich	22 Jul 1861, Peel River, NSW, Aust	1862, Sydney, NSW, Aust	0-1 years	Unknown - death record not obtained
Frederick John Rich	1863, NZ	1863, Tuapeka, NZ	<1 year	Unknown - death record not obtained
Henry Bindon Rich	1865, NZ	5th Jul 1865, Tuapeka, NZ	6 months 5 days	Acute hydroceptiales (sic) - I think it should be hydrocephalus
Sydney Rich	1865, NZ	1866, Gabriel's Gully, NZ	0-1 year	Unknown - death record not obtained
Emma Matilda Rich	unknown	1868, NZ	unknown	Unknown - death record not obtained
Sampson Rich	unknown	before 1872	unknown	unknown - only known from death record of mother
Alfred Rich	1868, Hokitika, NZ	7 Dec 1872, Melbourne, Vic, Aust	4 years	Bronchitis and whooping cough
Cornelia Rich	1870, NZ	21 Nov 1872, Melbourne, Vic, Aust	2 years	Debility and marasmus
Avice Rich	10 Mar 1872, Melbourne, Vic, Aust	2 Jul 1872, Melbourne, Vic, Aust	3 months 22 days	Marasmus and apoplexy
PLUS their mother:
Mary Jane Rich née Bindon	8 Mar 1838, Crowcombe, Somerset, England	8 Apr 1872, Melbourne, Vic, Aust	34 years	Anaemia and diarrhoea

Looking at this information, I'm not sure if syphilis could be blamed for any of these deaths. I had wondered if the children's mother, Mary Jane, could have died of syphilis, and I was talking to a health professional about this and she said it was definitely possible to die from it, but it would be tertiary syphilis, and she was too young for that. That Henry died from acute hydrocephalus makes me think it was from a congenital cause, resulting from parents who were first cousins. It is so sad to think of Mary Jane and William having baby after baby and watching them all die. Such sorrow. I can only imagine Mary Jane thinking about the babies in her womb, time after time, wondering and worrying about what might be wrong with this next one.