On one of our computers, the Security Tab in the Java Control Panel sometimes looks like this:
As you can see, the part required to manage the exception site list is missing/not accessible. I have no idea why (reinstalling Java did not help).
However, you can also add exceptions by directly editing the exception.sites file. Under Win 7, it is normally found in the C:\Users\*YOUR USERNAME*\AppData\LocalLow\Sun\Java\Deployment\security directory. Simply add a new line for each URL (e.g. https://stupdidbank.example.com), save the file, then restart the browser.