When you are in an Antistasi game, go back to your HQ, there's a mapboard (or I'd call it postboard since the word "map" confused me before) that has Antistasi's steam logo on it. Use scrollwheel to interact with it, select "Game Options", and then a UI should pop up where in its bottom there will be a bottom that says "Persistent Save". Click on that and you are done.

To load a Persistent Save, whenver you start playing the Antistasi scenario, there will be a UI pop-up asking if you'd like to load the previous session. Click "Yes" on that and you will load your latest persistent save.

For what persistent save does, refer to the antistasi wiki or the antistasi manual, just Google it