You just Need to create a check box with name remember.
It will do the rest. when the admin login form submit the corresponding task is written on the
administrator/compoenets/com_login/controller.php
You can find a function with name login()
Just check that code something like this.
$options['remember'] = JRequest::getBool('remember', true);
Also make sure cookie path are correct ,If you are working with subdomain sometime path will create issue.
Hope this may help you..