This FAQ is now obsolete as the latest Norton 360 does not manage cookies as before.
If you want your online login information not to be deleted by Norton 360 scan function, you have to change the Norton 360 tracking cookies setting under Settings > Antivirus > Scans and Risks. The setting Tracking Cookies Scan under Computer Scans can be set to Remove, Ignore, and Ask Me. Change it from Remove (default) to either Ignore or Ask Me (see the screenshot below). This will prevent Norton 360 from deleting your login information.
Please note that privacy and browsing history settings of different web browsers can also interfere with how you want your online login information to be handled.