By far the commonest disorder of this kind in children is ketotic hypoglycemia, which occurs in young children when the carbohydrate intake is reduced, often as a result of diminished appetite in a minor illness, to the point that fat stores are needed for energy and ketones are produced.

Increased blood glucose levels from the absorption of carbohydrate are balanced by insulin; but three other hormones (epinephrine and glucocorticoids from the adrenal gland, and glucagon from the pancreas) share the responsibility for restoring normal blood sugars from hypoglycemia, either by the breakdown of liver glycogen or by the conversion of protein or fat to glucose (gluconeogenesis). Acquired and congenital deficiencies of the hormones mentioned above, as well as certain inherited metabolic diseases, can also cause hypoglycemia. The possibilities are best elucidated though by an endocrinologist (for adults) or a pediatric endocrinologist (for infants and/or children) or by other specialists in inherited metabolic disease (which would usually be located at a medical school or major medical center) who has access to the sometimes complex laboratory support that may be needed.

Another hypoglycemic condition is called reactive hypoglycemia. It is manifest by a fall in blood sugar which causes symptoms during the period following meals. Simply put, the body has trouble braking the secretion of insulin after a meal, resulting in the blood sugar dropping further than it should. Reactive hypoglycemia is different from spontaneous hypoglycemia, which is not associated with meal ingestion. Reactive hypoglycemia generally has a benign prognosis.

Finally, it should be mentioned that many times, adults (and sometimes kids) have symptoms that seem to be about the same as hypoglycemia, which may have relief from food, but which are found to have completely normal blood sugar levels despite rigorous testing. This situation is seen as a normal reaction to severe stress, and sometimes in exaggerated form in disorders of anxiety or panic.

Also see

Other Causes of Hypoglycemia at the The National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) website. "Hypoglycemia in people who do not have diabetes is far less common than once believed. However, it can occur in some people under certain conditions such as early pregnancy, prolonged fasting, and long periods of strenuous exercise. People on beta blocker medications who exercise are at higher risk of hypoglycemia, and aspirin can induce hypoglycemia in some children. Drinking alcohol can cause blood sugar to drop in some sensitive individuals, and hypoglycemia has been well documented in chronic alcoholics and binge drinkers. Eating unripe ackee fruit from Jamaica is a rare cause of low blood sugar..."
Diagnostic approach to adults with hypoglycemic disorders. Service FJ Endocrinol Metab Clin North Am. 1999 Sep;28(3):519-32, vi. Review. "Optimal conditions for confirming the presence and accurately diagnosing the type of hypoglycemic disorder occur at the time of a spontaneous spell. Otherwise, dynamic testing to generate conducive conditions should be conducted in any patient with a history of neuroglycopenic symptoms, regardless of relation to meal ingestion. Specific criteria regarding beta-cell polypeptide concentrations are required to establish hyperinsulinemia. Sulfonylureas in plasma should be measured with sensitive assays. In complex cases, the selective arterial calcium test may be a useful dynamic test."
Classification of hypoglycemic disorders. Endocrinol Metab Clin North Am. 1999 Sep;28(3):501-17, vi. Review. "The classification of symptoms of hypoglycemia, namely, reactive versus fasting, based on segregation by timing in relation to meals is no longer useful from a clinical point of view. Every patient with neuroglycopenic symptoms, regardless of relation to food ingestion, requires comprehensive evaluation. Identification of the possible cause of hypoglycemia and selection of diagnostic modalities are facilitated by considering whether the patient appears to be healthy (with or without compensated coexistent disease) or ill (with a disease known to have a proclivity to develop hypoglycemia, or is hospitalized). Medications may mediate hypoglycemia in anybody, whether they appear healthy or ill."