OS X has user accounts, that either have Admin or Limited access.
You need to use an Admin OS X account with EyeTV, when you setup EyeTV, so that your channels and preferences will be remembered.
Go to the System Preferences > Accounts, and change your account to Admin access, under the Security tab.
Then, setup EyeTV. Quit and restart EyeTV for the changes to stick. Then, you can change the account access back, if you like.
As of EyeTV software version 1.8.3, EyeTV will automatically ask you for an administrator password when launching the Setup Assistant in order to be able to save channels and settings permanently.