How to prevent the dwarf children from going missing or dying of dehydration

Babies need their mother to carry and nurse them, and so will die if she is hospitalized or unconscious for too long - keep women (or mothers of infants, if you can be bothered with the micromanagement) out of hazardous professions like the military, mining and, to a lesser extent, masonry if you wish to avoid infant deaths. Children, on the other hand, can eat and drink for themselves. Unless you happened to assign all of the children to a separate sleeping wing and "accidentally" wall them in, there should be no reason for children to die of hunger or thirst except famine and drought.

Keep in mind that children don't actually serve a purpose besides slight happiness boosts to the parents (nothing a grand dining room won't exceed a dozen times over), pulling levers and deconstructing constructions; coupled with the fact that your fortress will probably crumble or become boring before they become teens this makes them very disposable indeed.