My mother has had these rather often, especially the last several years. Perhaps it is stress related to her job as a child care provider (or child development manager, whichever term you'd care to use). She has told me that they really started after she gave birth to my sisters, but that they were not connected to any given child.
My personal thoughts are that they are a form of night terrors, a vague sense of fear without the solidity of a nightmare.
To look at ScottMGS's experiences: some danger is presented, but now he has another being to take care of besides himself. Perhaps in the dream, he takes care of himself, but does not remember the child until after he has come awake and can reason about the danger.
eldritch's case does not parallel nicely with my mother's, but perhaps her comment about it occurring near times of stress lends itself to the idea. It may be just a general feeling of loss, that she must recover, and her mind interperates whatever signals it is getting that the object of loss was a child or child-like. Again, whatever stimulus is given, she may think that she has not provided for this other being once she has escaped from the danger.
I suppose my 2 cents worth exchanges to around $0.0175, but I give it freely.