Translated terms are not searchable with Search API
I think that this is core issue that the search index does not add the localized term to the index, I solved that by implementing hook_node_update_index($node) and fetching the localized term name by querying it from database because I don't know why i18n_taxonomy_localize_terms function doesn't load the term properly. my code is below:

function mymodule_node_update_index($node) {
  $text = '';
  $tid = key($node-&gt;your_taxonomy['und'][0]['tid']);
  if($tid != 0) {
    $query = db_select('locales_target', 'lt');
    $query-&gt;addExpression('CONVERT(translation USING UTF8)', 'translation');
    $query-&gt;join('locales_source', 'ls', 'ls.lid = lt.lid');
    $query-&gt;condition('context', 'term:'.$tid.':name');
   $text = $query-&gt;execute()-&gt;fetchColumn();
  }

  return $text;
}


Note: in my case the text is Arabic so I converted the field character set from blob to utf8.