Not sure what's going on, but you could try the following as a temporary workaround for after you close the game.
1) Locate your Starsector installation folder, see if it has a "vmparams" file (with no extension) in it. If so, open it in a text editor of choice.
2) Locate the "-Xms512m -Xmx512m" part of the text, and change that to "-Xms1024m -Xmx1024m".
3) Save the edited file. Be sure that it's saving over the original file -- you may have to toggle showing file extensions to on if you're using Windows, see Google for specific steps.
4) Start the game and see if it loads the save.
Keep in mind that I can't guarantee this working, and it may well start messing up again at a later point in time once your new limits start being exceeded. Consider this a final thing to try, and maybe wait for Alex to reply first.