You can simply pause any game that you don't want to advance in time (Main Menu/Options). You can also back up the savegame files to preserve them. The savegame files (in the Windows version) are located in Program Files\Fish Tycoon and are named FishSaveGame1.pts through FishSaveGame5.pts (corresponding to the player slots). Just pause the game(s) and back up those files to another folder of your choosing.