How do I allow my post to update it’s date every week

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You can use cron-jobs and there’s 2 ways you can do that:

  1. wp_schedule_event($timestamp, $recurrence, $hook, $args);
    http://codex.wordpress.org/Function_Reference/wp_schedule_event

    The action will trigger when someone visits your WordPress site, if the scheduled time has passed.

  2. Server cron job