AuthManager offers support for allowing a user to remain logged in beyond the current session. If the "rememberMe" parameter is sent back with (any) value with the login request, the server will return a login cookie for this purpose.

So, this task consists of:
-Adding a "remember me" checkbox to the login layout and updating the API request based on its contents;
-Testing to ensure that the login cookie is returned and handled as expected and the login persists across sessions.

http://authmanager.wmflabs.org/w/api.php?action=query&meta=authmanagerinfo&amirequestsfor=login