Why using of custom date format makes my Drupal date outdated and does not change at all?
Instead of manually inserting stuff in the database, make use of the Drupal API. The blog post Exporting and maintaining custom date formats in Drupal 7 is a great tutorial. It's geared towards modules but I'm pretty sure you can do this in an install profile too.

I think this will solve your problem, and even though I'm not 100% sure, I would always recommend to use the API.



Here's a quick copy-paste of the most important code from that blog post, just in case the link would break in the future:

/**
 * Define and export date formats.
 */

// Give the date format type a machine name.
define('MODULENAME_DATE_TYPE', 'MODULENAME_date_type');

// Define the string to be passed to date().
define('MODULENAME_DATE_FORMAT', 'l, jS M Y ');

/**
 * Implements hook_date_formats().
 */
function MODULENAME_date_formats() {
  $formats = array();
  $formats[] = array(
    'type' =&gt; MODULENAME_DATE_TYPE,
    'format' =&gt; MODULENAME_DATE_FORMAT,
    'locales' =&gt; array(),
  );
  return $formats;
}

/**
 * Implements hook_date_format_types().
 */
function MODULENAME_date_format_types() {
  $types = array();
  $types[MODULENAME_DATE_TYPE] = t('Default date for MODULENAME');
  return $types;
}


The blog post also provides a utility function to clean up old, unused date formats:

/**
 * Delete cruft date formats from the database and resync date formats/types.
 *
 * Call this as often as required to ensure date configuration stays in-sync.
 * Don't call this on every page load. hook_flush_caches() or hook_update_N
 * are good candidates.
 */
function _MODULENAME_purge_date_formats() {
  $formats = system_get_date_formats(MODULENAME_DATE_TYPE);
  variable_set('date_format_' . MODULENAME_DATE_TYPE, MODULENAME_DATE_FORMAT);

  // Date formats without a dfid are being read directly from code. We can use
  // the existence of this value to detect "ghost" formats that are not managed
  // in this file.
  if (!empty($format['dfid'])) {
    system_date_format_delete($format['dfid']);
  }
}