Normally a low glucose level will trigger release of an enzyme called Glucagon, and this is the signal to the liver to start creating glucose from whatever is lying around. i.e. gluconeogenesis will use proteins, ketones snippets of lipids and anything that looks like it could make something useful for the brain.. It seems this process may not be working correctly.
you may be going into ketosis and using lipid fat for energy instead of glucose through the process of lipolysis. When you hypo, do you have other symptoms of hypo, or is it just going by meter readings.