Once you enter the API key and Secret, they are encrypted in the .ini file. Previously the password they were encrypted with was hardcoded, not user-choosable and I found this odd (security hole). So I cobbled together the method that you see in my forked version, and heres the instructions.
1) Download the fork from https://github.com/genbtc/goxgui
2) The program will generate a new blank config file on first run. (Don't try to import the old one)
3) Click the Options Menu, go to Preferences, and enter your API Key and Secret
4) Enter a Password of your own choosing.......
5) Hit Apply to check for errors, and then click OK if verified.
6) The program will encrypt the API Key/Secret and store it in the INI file.

This will store your password, and auto-login everytime you launch it next time.