The liver and muscles store enough glycogen to last hours

I think the answer would be around 6-24 hours

Glycogen will be broken down into glucose that becomes the main supply of energy around 2 hours after eating(postprandial) period. The effect should be declined after 12 hours, which is why fasting glucose is taken around that time. After the glycogen depleted, the blood sugar will keep become lower and the body will start making glucose using protein or lipid.