Note that the story will be designed in acts or "episodes" each lasting approximately 8 hours, which will make the breaks fit naturally into the drama. This design is something we would have done anyway, BSG is TV-series after all. To break up a larp in acts with "off time" in between is maybe not the most common larp design, but it has been done many times with good results. A complete break also avoids 48h shifts for the game masters...
The alternative would be to look for another place altogether which would throw the production into a new void of uncertainty, a place we'd like to reserve for the characters once the game starts :)
Another one would be to leave the ship in smaller groups to sleep in turns and leave the game running. Our opinion is that this has more drawbacks than a common break. It requires more logistics, some will have odd sleeping hours, less rest for game masters and most of all it can become strange that all characters are not available all the time.
If you have any strong opinion about this please use the comments. We'd be happy to get your input.