You can use an event subscriber for that, and attach it to the ORM event listener (in symfony 2, there's docs about that):
namespace YourApp\Subscriber;
use Doctrine\Common\EventSubscriber;
use Doctrine\ORM\Event\OnFlushEventArgs;
use Doctrine\ORM\Events;
use YourApp\Entity\Issue;
use YourApp\Entity\IssueLog;
class IssueUpdateSubscriber implements EventSubscriber
{
    public function onFlush(OnFlushEventArgs $args)
    {
        $em  = $args->getEntityManager();
        $uow = $em->getUnitOfWork();
        foreach ($uow->getScheduledEntityUpdates() as $updated) {
            if ($updated instanceof Issue) {
                $em->persist(new IssueLog($updated));
            }
        }
        $uow->computeChangeSets();
    }
    public function getSubscribedEvents()
    {
        return array(Events::onFlush);
    }
}
You can eventually check the changeset as I've explained at Is there a built-in way to get all of the changed/updated fields in a Doctrine 2 entity.
I left the implementation of IssueLog out of the example, since that is up to your own requirements.