Dalrymple reports on a recent article in the Lancet that tries to address this question:
Various motives have been suggested, by no means mutually exclusive. An excessively anxious mother may exaggerate or fabricate symptoms in order that the doctor pays more attention to the child. She may wish to have her beliefs about the child’s health confirmed, in some cases beliefs that are frankly delusional. The mother may wish for attention, hence needing to dramatize her child’s condition. She may wish to maintain a pathological closeness to the child and keep it in a state of complete dependence. Finally, the social security system may provide money for mothers with sick children.