Recently, a 2-month-old baby passed away ל"ע, and the family indicated that there would be no shiva.
Under what circumstances is there no shiva for a baby that lives passed 30 days?
My understanding is that 30 days was considered a rule of thumb for whether we call this a healthy baby that could have lived, but then died; vs. a sign that this pregnancy was never truly viable.
Traditionally (for instance Chochmas Adam 161:6), the understanding was that an "eight-month-gestation" baby was born with severe defects and thus never got Shiva, even if it survived 30 days; whereas if we were positive that this baby was a healthy, viable, "nine-month" baby that was killed ל"ע by a gunshot or something within 30 days, there still would be shiva.
I would assume -- and obviously, a serious posek would have to be consulted on each case -- that if a baby was born with severe, severe defects that everyone would agree was not viable, but the heroic measures of today's medical technology managed to keep it alive for a few weeks (managing its breathing, temperature, electrolytic balance, and the like), we would call that akin to the traditional case of an "eight-month baby" and not observe shiva. But don't ask me exactly where we draw the line.