Submit handler is not getting called inside theme function
It looks like you are declaring your submit button's submit handler correctly. Rather than debugging with print(), try using drupal_set_message() or the Devel module's dpm().

Example with drupal_set_message():

function user_content_ranking_save($form, &amp;$form_state) {
  drupal_set_message('Submit handler was called.');
}


Edit:

Also, if you are constantly refreshing the same form, Drupal may have cached it. Try clearing your cache and see if your submit handler is now being called.

Answer:

Are you sure the whole form is being rendered when using your theme function? It may be that the form is not being validated because the rendered output of the form does not contain the form_id, form_build_id, and/or form_token.