There are log files that refresh every time the game is closed. If this happens again can you follow this link in Internet Explorer to gather those log files before reloading the game:
http://sd.stardock.com/Demigod_report.zip
Save the file, run it, and attach the .zip file (located under YOUR USERNAME\My Documents\My Games\Gas Powered Games\Demigod\report) it generates to an e-mail to [email protected]
Some email providers won't allow you to send certain files; if it won't allow the file to send, you'll need to slightly modify the file extension(for example change .zip to .zii).