I'm the programmer on this game. It's not supposed to lose save data between sessions. It stores your saves in the cosmo.sav file, which should be in the same folder as the game exe.
The first thing that comes to mind is that the game might not be able to create the cosmo.sav file if it's on your desktop or something. You could try moving your installation to a different folder. If you have the game folder open, you should see the cosmo.sav file appear shortly after you enter the name for your first save.