Web application - localstorage problem only on iphone

Web application - localstorage problem only on iphone

Hello, 
I am a french developer, and I have made a web application with html5, css3, jquery 1.8.3, jquerymobile 1.2.0 :


I use theses functions to register and get infos from/to localstorage : 

function registerDataToLocalStorage(pmKey, pmValue) {
   removeDataFromLocalStorage(pmKey);
   localStorage.setItem(pmKey, JSON.stringify(pmValue));
}

function removeDataFromLocalStorage(pmKey) {
   localStorage.removeItem(pmKey);
}

function getDataFromLocalStorage(pmKey) {
   return JSON.parse(localStorage.getItem(pmKey));
}

I tested my application on my Samsung Galaxy S2 - worked
I tested on navigators Safari, Chrome, Firefox - worked
I tested on iphone / ipad - bug :

It's seems to be a thing like : 
the first time I use the application on iphone / ipad, I register value Step = 4
when I use in the future, when I get "Step" it will always get value 4, even if I change the value between.

It's really strange, because i tryed on in other devices it works fine.

Someone has a idea to help me please ?
Thanks a lot.

PS : The iphone which one I tested the application is iphone 5.


EDIT : I have tested the application on iphone 4 with Safari 5.1.1 and worked, so it seems to be a 6.1.1 problem only.