Is this a file geodatabase? I get errors when attempting to zip a fgdb when someone has it opened. As it creates some lock files that are opened exclusively and cannot be accessed by other applications. I really wish there was a way to make ArcMap/Catalog close gdbs when they've stopped using them and not just when you exit the app. At least with SDE databases you have a disconnect option. No such thing with pgdb and fgdbs. As it is, I always have to make sure I close out of ArcMap/Catalog before zipping a fgdb to avoid this.