Is your computer doing something every several days? Perhaps an automated temp file cleaner or something is interfering with DD? Have you installed anything lately (around when the problem started) that either does something periodically, or is always running?
Are you shutting down all non-essential programs (especially anti-virus) before starting the game?
If the game was encountering a problem while exiting, it should not matter how long you wait before trying to start it again. DD uses an entry in a file generally used for install programs (called ntsetup.bat, or something like that) to delete a temporary file the next time the computer is booted. If you reboot your computer after exiting the game, does that trigger the error? That file is the only thing within the game itself that should be time sensitive, AFAIK.
In the configuration program, you do not need to rerun the test each time. Check the 'skip test' box, then click on the 'test' button and it will immediately change to the 'apply & close' button.
Other people have run into problems with the game on exit, but either randomly or consistently (one person had DD crash every exit), rather than being time sensitive, IIRC.
BTW, since the problem is with the game itself, if it ever refuses to start after resetting the configuration you should just be able to backup your saved game folders (just in case) and do a clean un-install and re-install to get it working.
Troubleshooting Tips (& manual install procedure)