Illustrator can only save the preferences when it is being run by the administrative user who installed it. You might be able to get around this by opening full read-write permissions on the preference files for all users.
To do this, select the file:
/Library/Preferences/com.adobe.Illustrator.plist
then, choose File -> Get Info.
Open the Ownership & Permissions section.
If the options are greyed out, click the padlock button and enter an administrator password.
Set group access to Read & Write.
Now, it should save preferences if any administrator is logged in.