No, it does not have to be on 24/7. However, if you advertise you are starting a Pitboss game and you do not intend to leave it on 24 hours a day then you should make that very clear, as well as pointing out just when you plan on having it on.
It will be assumed that the game is to be run 24/7, minus downtime for glitches, computer resets, etc. This assumption is reasonable since it gives players the most flexiblity about when they can play their turns, and takes the functionality of the Pitboss program to its logical extent. But it isn't required by any means, as you can load and save pitboss games very easily.
