I think that you need to specify a fixed local_server_port in your rhoconfig.txt file:
By default, Rhodes apps uses random TCP/IP port and every time you restart your app you're working with a different local storage because they are linked to <tcp/ip address>+<tcp/ip port>.
Just remember that you cannot have two application running on the same devices trying to bind a server to the same tcp/ip port.
It's probably not lost - it's accumulating. The WebView sees each different random port as a different "website".
But don't understand the need for Localstorage - that's what Rhom is for.