How reliable is hook_post_action module? I am using this module under Drupal 7 to execute some code after nodes of a particular content type get updated. My question, is this module reliable? Would the post save event be called every time my target nodes get updated?

This is the module's page:
https://www.drupal.org/project/hook_post_action
The module register a shutdown function in hook_entiyt_delete(), hook_entity_insert(), and hook_entity_update().  

/**
 * @param $entity
 * @param $type
 */
function hook_post_action_entity_insert($entity, $type) {
  drupal_register_shutdown_function('_hook_post_action_post_save', $entity, $type, 'insert');
}


As such, the hooks invoked from that shutdown function are always invoked, except in the case the shutdown function is not called, which as the documentation for register_shutdown() says, it can happen if the process is killed with a SIGTERM or SIGKILL signal. Since PHP doesn't have a function to removed a shutdown function, I would say the module is reliable.

As side note, hook_node_postsave() and hook_entity_postsave() are always invoked, whenever the entity is created, updated, or deleted.

/**
 * @param $entity
 * @param $type
 * @param $op
 */
function _hook_post_action_post_save($entity, $type, $op) {
  $entity_is_saved = FALSE;
  $new_entity = NULL;

  if ($op == 'insert' || $op == 'update') {
    $entity_is_saved = TRUE;
  }
  if ($op == 'delete') {
    list($id) = entity_extract_ids($type, $entity);
    $new_entity = entity_load($type, array($id));
    if (!$new_entity) {
      $entity_is_saved = TRUE;
    }
  }
  if ($entity_is_saved) {
    module_invoke_all('entity_post' . $op, $entity, $type);
    module_invoke_all('entity_postsave', $entity, $type, $op);

    if ($type == 'node') {
      module_invoke_all('node_post' . $op, $entity);
      module_invoke_all('node_postsave', $entity, $op);
    }
  }
}