Experience and skills aren't meant to persist across runs, so that's intended behavior (the same way it works in the story, Liz will have to earn her skills in each timeline).
I'm much more concerned about the save file issue. Are you running this locally or on a VM? Any user account weirdness that'd interfere with saving files to AppData? You can check C:/Users/(your name)/AppData/LocalLow/Anunnaki Games/New Pred in Town/NaninovelData/Saves to see if files are being recorded at all.