I have never had a child die unless it was with the whole village.That was because I had just started and I didn't check back with them for awhile.
But I had a child die when the mother died.
But when you were absent from the game,if you were absent for awhile it doesn't take much for a villager to get sick.
I take a look at the red bar at the top of the detail screen,and if they have lost any part of their life meter,I keep a close look in on them.
Sorry though!
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You cannot do a kindness too soon, for you never know how soon it will be too late.