Yes! Redownload the newest version of the game to a new location. You can go into your old Asagao Academy folder and inside the "game" folder there's a folder called "saves". Right click and copy that entire folder. Then go into your new Asagao Academy folder and paste your saves folder into that version's "game" folder (note that if you haven't started up the new version of Asagao at least once, there wont be a "saves" folder inside the games folder. That doesn't matter! You can paste the saves folder in there anyway and it'll work.)
Alternatively, you can just overwrite your old Asagao Academy folder with the newer version and it'll replace all the files that need to be replaced and still keep your saves. If you do it this way, I recommend making a copy of your Asagao folder beforehand, just in case.