Webstorage is the browser storage, if the cache isn't deleted, it should stay (even on node-Webkit)
And for the Node Webkit plugin, you can save a file with data in a folder on the user computer, and also load a file, so, it works offline
(the node-webkit plugin is still in beta though, so you may take that in consideration)
Hope that helps
And that is why you shall respect the bug reports guidelines, not only giving a capx is making the bug reproductible in one click in a situation they can work with (less time wasted trying to reproduce vague instructions) but also it helps filtering false positives.
Game design is all about decomposing the core of your game so it becomes simple instructions.