A few weeks ago I have the same problem. I also don't know how to use the webstorage correctly. There is a lack of examples on this
Anyway, here is my capx were I am able to save and retrieve data from the array.
Run the capx, click on some buttons and do save, refresh browser, click load. Voila, data is back!
These are event based, so you can use it for On layout load to do the trick instead of having to push the load button.