How strange. Here is what I’ve just done, using Firefox:
1. Deleted all the cookies
2. Set English as “preferred” language of the browser
3. Closed the browser
4. Reopened the browser and typed the address of my home page
5. The English version appeared
6. Checked the cookies: there is one named “wordpress_polylang” with value “en”
7. Closed the browser
8. Reopened the browser
9. Checked the cookies: the cookie named “wordpress_polylang” is still there with value “en”
10. Typed the address of my home page
11. The ITALIAN (default) version appeared!!
12. Checked the cookies: now the one named “wordpress_polylang” has value “it”!!
I don’t know where the problem is: faulty browser or what?