Cooked mug cake really needs to be eaten straight away. It really is at its best then - steaming hot and delicious. Additionally, when left to cool, don't expect it to cool into a standard fluffy cake. Given that it's nuked in the microwave and steamed, rather than baked, the texture will start to harden as it cools, which isn't great.
You could make the batter up to a day in advance and store in the fridge before microwaving, however. Just make sure to give it another good stir before cooking in case the ingredients have separated.