When you are opening the files locally, i.e. using the file://
protocol, as of now the browsers can not determine what is “same domain” so every file is considered a separate domain. Thus you can not use localStorage
when you’re opening the files.
Here is some more information on the problem in FireFox: https://bugzilla.mozilla.org/show_bug.cgi?id=507361 . Personally I couldn’t find much about Safari on this topic.
You can also look over this: Javascript/HTML Storage Options Under File Protocol (file://) . It might be helpful in your situation.