Now I'm prefacing this with the fact I tested on Windows 10 and it worked, just need someone to test on Windows 8.1 and lower for 100% evidence across all major Windows platforms.
The reason why you can't save when the game is installed in the Program Files folder is due to permissions. At the very least Windows 10 is affected by this.
What I did was add myself as the owner and as an additional user to the folder then granted myself full control of the "Shiny Days" folder in "Program Files (x86)". See the following link(s) for information on how to do this. Keep in mind this is the most secure why of doing it as you're not giving rights permission to all of Program Files, only the Shiny Days folder specifically.http://www.askvg.com/guide-how-to-take-ownership-permission-of-a-file-or-folder-manually-in-windows/http://answers.microsoft.com/en-us/windows/forum/windows_8-security/im-an-administrator-on-windows-8-but-still-get/2aed6083-b986-4423-90bb-986749bc236b?auth=1
I'll be happy to assist if anyone has trouble doing this. Once you have set the permissions, go ahead and launch the game. Save to any slot to see if it works.
Again this worked for me on Windows 10. I no longer have any Windows 8 or 7 machines in the house to test, so if someone can, test and post here with the results. Thank you!