How could this possibly work? What's the mechanism?
Do the sperm heading towards the unfertilised egg, somehow know, based on their sex chromosomes and the sex of previous/existing children, to quit?
Does the mother's body in some way reject the inappropriately sexed sperm, though morphologically I believe female and male sexed sperm are incredibly similar? How would it be possible to discriminate in this way against some sperm and not others?
Or is there some kind of effect causing die off of inappropriately sexed sperm in the father-to-be's balls? Are his balls able to tell the sex of existing children, and not only that, but remember the order in which they were born?
What would be the reproductive value in any of these proposed mechanisms? I'm curious as to what selection pressure could be at work that would overcome the disadvantage of inactivating 50% of potential sperm?
Are you perhaps suggesting that there is an increased propensity to early spontaneous abortion of inappropriately sexed embryos for some reason, relating to the birth order and sex of existing children?
If any of this were plausible, how could the same dad have anything to do with it? You're suggesting that the sperm and/or female environment possess some kind of knowledge of / are influenced by not only the sex and birth order of existing children but their parentage as well?
What are the confidence intervals of your prediction and are the number of families you are aware of with 3 children (your sample size) great enough to attribute the results of your observation to a genuine effect rather than chance? I rather doubt this.
For the record, I have BGB.