The objects of the senses turn away from an embodied person who abstains from them, but the taste for them remains. Even that taste fades for one who has seen the Supreme.
Explanation
Krishna is describing the person of steady wisdom (sthitaprajña) to Arjuna. Merely staying away from sense objects (viṣaya) is not enough, because the inner craving or taste (rasa) stays behind. Only the direct realization of something higher (paraṁ) ends the craving itself. Traditions differ on what "the Supreme" is: Advaita reads it as the Self (Ātman) or Brahman, while devotional schools read it as God.