Another technical fix: 
This seems so obvious that I am ashamed to have taken so many years to come up with it.  First recall the Iceland data, consisting of two graphs of fertility graphed against kinship for children:

and grandchildren:

An Association Between Kinship And Fertility of Human Couples.  Agnar Helgason, Snaebjoern Palsson, Daniel F. Guobjartsson, Pordur Kristjansson and Karl Stefanson, SCIENCE vol 329 8 February 2008 page 813 figure 3 C. 
Relative growth rate on the vertical axis, degree of kinship on the horizontal.  In each case the first entry is “second cousin or closer” or first cousin once removed.  So the degrees of separation are a half notch off.  No matter.  Also kinship is not reckoned by the nearest connection but by the sum of all connections.

Right.  We see that maximum children are at the closest alliance measured; maximum grandchildren are at third cousin.  The curves are of about the same intensity and fall off at about the same rate, the only big difference being between very near kin. 

Now since both children and grandchildren are affected, we shall assume that there are both a pre-zygotic mechanism of infertility and a post-zygotic. 

The process of in vitro fertilization, or injecting the sperm directly into the egg has about a fifty-fifty chance of producing a baby.  This process bypasses any pre-zygotic safety check, but it does nothing at all for any post-zygotic infertility.  That is to be expected if pre-zygotic and post-zygotic effects are about balanced, as we would expect from the Iceland data. 

In vitro fertilization has been around for about thirty years.  Millions are alive today because of it.  So by now there should be lots of babies who have a parent who was herself or himself the result of in vitro fertilization. 

But when I searched PubMed and Google for cases, I found none.  It would seem that somebody should be crowing, and the lack of crow suggests lack of a case.  (Searches for “in vitro fertilization” and “cousins” also gave no joy.)  So the worry arises that perhaps because of accumulating post-zygotic infertility all children of in vitro fertilization are infertile, even if they are themselves offered the in vitro fertilization process. 

Until now, some ghoul in my head has whispered, “And they always will be.  Abandon hope that in vitro fertilization will restore a viable birth rate.”

But my ghoulish tormentor distracted me from the possibility that it might not always be true.  There might be an easy fix.

If a man or woman who is an in vitro fertilization baby wants to have a baby it’s possible, just barely possible, that this could be achieved as it has never been achieved before simply by choosing an egg or sperm from an appropriate relative.  Anonymity might be accomplished for the male donor by collecting sperm from every single male relative and concealing for a time which one was the real donor.  Doing the converse with women would be much more problematic, of course. 

The ideal paring for grandchildren in the Iceland data is third cousins.  But that is a compromise balancing the sky high fertility that close kinship offers by avoiding the pre-zygotic mechanism and the optimal kinship for avoiding post-zygotic infertility, which is probably less closely kin.  With in vitro fertilization available, pre-zygotic effects are less feared, so it might be prudent to back off to something like fourth cousins in order to achieve the optimal offspring in adequate numbers.

Alas it might not be so simple.  There is evidence that the in vitro fertilization process (Michael R. DeBaun et al. Association of In Vitro Fertilization with Beckwith-Wiedemann Syndrome and Epigenetic Alterations of LIT1 and H19 THE AMERICAN JOURNAL OF HUMAN GENETICS Volume 72, Issue 1, January 2003, Pages 156-160) causes epigenetic changes (changes in the mechanisms that turn genes on and off), which probably lie at the very heart of the phenomenon of infertility secondary to an improper degree of kinship. Increasing those changes might well cause absolute infertilty every time.  

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