This is really an odd problem. So it opens and correct the first time and then doesn't again afterwards. That could only when you exit, something gets written to the files in a incorrect way then it cannot open again.
I have never tried Black Package games on Windows 8. I have gotten them working on Windows XP and Windows 7. I prefer to use mostly a Windows XP VM on Windows 7 because some games are so dependent on Japanese settings on the Operating System that it's too much trouble trying to switch between Japanese and local settings.
Because I am using Windows 7, I have a license Windows XP mode from Microsoft.
http://windows.microsoft.com/en-us/windows7/install-and-use-windows-xp-mode-in-windows-7
As far as I know they discontinued the free Windows XP license for VM with Windows 8. But there is a workaround to get it setup.
http://lifehacker.com/5965889/how-to-run-windows-xp-for-free-in-windows-8
Even with the Windows XP VM, I had quite a lot of problems getting Black Package games to work. At the end of the day setting most of the regional, local and date time settings to Japanese solved my problem. I nice user on this forum helped to read the error messages I was getting and pointed out that even though I have had a ton of stuff set to Japanese, it was still lacking some.
Link to the forum post
This was the final setting that helped me get all Black Package games working on the XP VM.
The date, time and currency format has a great impact on most applications in Windows because if a program call "date" Windows will give the value in the format that it is set to. This area might be the problem you are looking at. When Black Package games closes it probably is making a time stamp somewhere then can't read it in the desired japanese format when opening again.
I would suggest to first go down the VM route so you have an OS you can mess with and not worry about making mistakes that could cause your primary OS problems. Then when you finally get the BP games to work fine on there you can start looking at the getting them working in you OS. Although I since have been keeping all the games in the VM merely because It's all contained in one place. If I ever need to re-install my primary OS, I just copy over my existing VM and no re-installs needed for any games.
Good luck and let me know if any of this helped you.