That old chestnut! It *always* takes more heat to keep something hot than to let it cool and then reheat it, basic physics. The heat lost is proportional to the (4th power of?) the temperature so if it's hot all the time it loses (a lot) more heat than if it's allowed to cool.
The better the insulation then the less the difference is, so if you had 'perfect' insulation then there would be no saving if you turned it off (and it wouldn't get any cooler if you did of course).