The Shulhan Aruch (Yoreh De’a 263; listen to audio recording for precise citation) addresses the tragic situation of a couple whose baby boy died as a result of being circumcised, and then had a second baby boy who also died after circumcision. After two boys in a family die as a result of Berit Mila, the Shulhan Aruch writes, it can be assumed that infants in this family are too fragile to survive a Berit Mila. Therefore, boys born subsequently are not circumcised, given the potential risk to their lives. They are circumcised only after they grow older and can be presumed physically capable of recovering from the procedure. Although generally a "Hazaka" (halachically recognized pattern) is established only after three occurrences of the same phenomenon, in this instance, when a risk to human is at stake, two deaths suffice to establish a "Hazaka" of the family’s inability to survive circumcision in infancy.
The Shulhan Aruch adds that this applies even if the two brothers who died as a result of circumcision shared only the same mother but not the same father, or the same father, but not the same mother. Meaning, if a man had two babies from two different wives, and they both died as a result of a Berit, or if a woman had two babies from two different husbands, and both died as a result of a Berit, the future sons of that man or of that woman are not circumcised during infancy.
Moreover, the Shulhan Aruch writes (based on the Rosh) that if two sisters both had babies who died as a result of Berit Mila, then the future sons of all the sisters are not circumcised during infancy.
Rav Yosef Shaul Nathanson (1808-1875), in his Sho’el U’meshib (Mahadura Kama, 1:238), writes that this law applies even to twin brothers who died as a result of circumcision. Although one might assume that they died as a result of special frailty due to the fact that they were born together, Rav Nathanson rules that their deaths establish a pattern that requires postponing the circumcision of future children born to their parents.
Finally, the Shebut Yaakob (Rav Yaakov Reischer, 1661-1733) writes that if a couple had two sons who died as a result of Berit Mila, and later they divorced and both remarried, their sons born with their new spouses are not circumcised during infancy. Since each one had produced two boys who died as a result of a Berit, each spouse’s subsequent children are not circumcised until they grow older.
It must be clarified that when a circumcision is postponed due to the deaths of two older brothers after undergoing Berit Mila, the child is circumcised when he grows older only if it is medically ascertained that the condition affects only infants. If the problem is found to be hemophilia or some other disorder, which poses as much danger in older ages as in younger ages, then the child is not circumcised at all, even when he grows older. As always, the Torah’s concern for human life outweighs all other considerations, and thus even the vitally important Misva of Berit Mila is suspended when there is even a small concern for the child’s safety.
Summary: If a mother or father had two boys who died as a result of Berit Mila – even with two different spouses – then the parent’s subsequent children are not circumcised until they grow older. This includes subsequent children produced with a different spouse. This law applies even if the two brothers who died were twins. If it is suspected that the condition is hemophilia or some other medical problem that is not resolved when a child grows older, then the child is never circumcised, due to the risk involved.