I just want to clarify Chris' post above. When a diabetic cat (or anyone) experiences extremely low BG numbers, the ensuing response is NOT because the organs presume they are starving. The excess insulin is moving whatever glucose that's in the bloodstream into the cells which is why when you measure BG, the numbers are low.This is because there is an excess amount of insulin and not because there's no available food. We can presume that this makes our cats hungry -- and if food is available, they will spontaneously eat. It is also not a response that is confined to the liver. Both the liver and pancreas respond to low numbers in a method that is protective. Every organism needs glucose to live. Thus, when BG drops too low, the liver and pancreas react by releasing glucagon and counterregulatory hormones. These substances cause a sharp rise in BG in order to protect your kitty from low BG levels. This spike in numbers is what we refer to as a bounce.
With starvation, the response is somewhat different in that stored fat and protein are part of the response. When fat and protein are being metabolized, ketone bodies appear in the blood. Glucagon stores are depleted within 24 hours in humans -- probably less time in cats since their metabolism is faster. It's useful to keep in mind that you're not starving your cat. With diabetic hypoglycemia, there's an excess of exogenous insulin rather than an absence of food.