Hate to pick nits but most human characters would become extremely sick. The longest anyone ever stayed awake on record was 18 days, 17 hours, and he probably had trained for it. One week would make people delirious, irritable, irrational, achy, have effects similar to psychosis, and more. Doing that would harm puppets more than it would be fun for us to play.
I can see that for immortals and deity-like critters, but we've got humans here, and that would make them very, very ill. :/