Origin of the ThiruNaamam(Exalted Name) of Lord Narayana as Achyuta

Question

Sriman Narayana amongst his ThiruNaamams(holy names), is referred to as Achyuta. In fact, Sri Krishna is fondly referred to as Achyuta by Arjuna in the Bhagavad Gita.

Is there a narrative thread which pillars this ThiruNaamam within the context of the Mahabharata apart from the Gita?

Edit: Although the question focuses on asking for references from Mahabharata (which has been answered), I would appreciate any additional references from other scriptural sources for purposes of comparative understanding.

Answer 1

Here is how Krishna explains the name Achyuta to Arjuna in this chapter of the Shanti Parva of the Mahabharata:

The cessation of separate conscious existence by identification with Supreme Brahman is the highest attribute or condition for a living agent to attain. And since I have never swerved from that attribute or condition, I am, therefore, called by the name of Achyuta.

Here is how the Advaita philosopher Adi Shankaracharya interprets the name Achyuta in his commentary on the Vishnu Sahasranamam :

He was not shaken and is not and will not be shaken from his own glory; hence the name Achyuta. The Shruti (Narayana Upanishad 13) says "He is eternal, calm, and unswerving (Achyuta)." Lord also (Mahabharata Shanti Pava 343) says "I did not swerve from my path at any time before; hence I am called Achyuta by that act."

And here is how the Sri Vaishnava Acharya Parashara Bhattar explains the name Achyuta in the Bhagavad Guna Darpana, his commentary on the Vishnu Sahasranamam:

The one who does not get separated from such surrendered souls is called ‘achyutaH’ – the infallible. The scriptures say thus in this regard: “Since I never gave up anything in the past, I am called ‘achyuta’” “I never get separated from such a devotee” “I shall never forsake him; that will never happen”, et al. Etymology: Since Bhagavan never gets separated from His devotees, He is called ‘achyutaH’. Alternately, He is also called ‘achyutaH’, by whose grace the surrendered souls never face any shortcomings.

Answer 2

In this chapter of Shanti Parva of Mahabharata, in the Nãrãyaniya section; Lord Krishna himself speaks about why he (Vishnu) is called Achyuta:

The cessation of separate conscious existence by identification with Supreme Brahman is the highest attribute or condition for a living agent to attain. And since I have never swerved from that attribute or condition, I am, therefore, called by the name of Achyuta.