As per the Mahabharata Tatparya Nirnaya by Dvaita School preceptor, Anandatirtha aka Madhavacharya, the god Vishnu bestowed immortality (Chiranjeevi) and the position of Saptarishi for the next Manvantara on Kripacharya.
यदैव गङ्गा सुषुवेऽष्टमं सुतं तदैव यातो मृगयां स शन्तनुः । शरद्वतो
जातमपश्यदुत्तमं बने विसृष्टं मिथुनं त्वयोनिजम् ॥५६॥
Shantanu was out on a hunting spree when goddess Ganga delivered her
eighth son, namely Devavrata, and found two children in the forest,
who were actually the children of a sage called Sharadvata, but
abandoned in the grass fields of forest. The birth of these two twins
occurred in a non-parturition (ayonija) method from that sage
शरद्वांस्तु तप: कुर्वन् ददर्श सहसोर्वशीम् । चस्कन्द रेतस्तस्याथ
शरस्तम्बे ततोऽभवत् ॥ ५७ ॥ विष्कम्भो नाम रुद्राणां
भूभारहरणेऽङ्गताम् । हरेः प्राप्तुं तथा तारा भाऱ्या या हि बृहस्पतेः ॥
57 & 58. Once, while Sharadvata performing his ascetics duties, he suddenly saw
the apsara Urvashi and ejaculated, whereby his seed fell in a shrub of
grass, whereby there arose one Rudra, from among the eleven Rudras,
namely viShkambha, in order to become a helping hand in the effort of
Hari to reduce the overburden of earth. So also, Taara, the wife of
Brihaspati, also transfigured herself and emerged as a girl from that
shrub of grass, along with that baby boy.
तावुभौ शन्तनुर्दृष्ट्वा कृपाविष्टः स्वकं गृहम् । निनाय नाम चक्रे च
कृपाया विषयौ यतः ॥ ५९ ॥ कृपः कृपीति स कृपस्तपो विष्णोश्चकार ह ।
तस्य प्रीतस्तदा विष्णुः सर्वलोकेश्वरेश्वरः ॥ ६०॥
प्रादादेष्यत्सप्तर्षित्वमायुः कल्पान्तमेव च। स शन्तनुगृहे तिष्ठन्
देवव्रतसखाऽभवत् ॥ ६१ ॥
59 to 60. Filled with mercy Shantanu brought those two twin children home for
fostering, Shantanu named them Kripa and Kripi, where Kripa is
synonymous with the word mercy.
Kripa meditated on Vishnu, and that lord of lords of the worlds,
Vishnu, accorded Kripaacharya with longevity till the end of the era
(kalpa), and even with a place in the coming cycle of Seven-sage
constellation, Sapta-Rishi mandala.
पुत्रवच्छन्तनोश्वाऽसीत् स च पुत्रवदेव तत् । मिथुनं पालयामास स
कृपोऽस्त्राण्यवाप च ॥ ६२ ॥ सर्ववेदानधिजगौ सर्वशास्त्राणि कौशिकात् ।
तत्वज्ञानं तथा व्यासादाप्य सर्वज्ञतां गतः ॥ ६३ ॥
62 & 63. Kripaachaarya grew up like a son of Shantanu, and Shantanu too
fostered both the children, Kripa and Kripi, like his own son and
daughter. Kripaachaarya obtained the science of missiles from Gautama,
all the Vedas and scriptures from Vishwaamitra, and obtaining all the
philosophical knowledge from the Vedavyasa he became an
To Summarize, as per the Mahabharata Tataprya Nirnaya:
Kripacharya was an incarnation of one of the eleven Rudras of god Shiva named viShkambha (विष्कम्भ).
Kripacharya performed austerities, meditating on god Vishnu, and thus happy with his penance, Vishnu bestowed longevity till the end of the Kalpa (Chiranjeevi), and also the position of Spata-Rishi fro the next Manvantara.
According to the website of speaking tree, Krishna made him immortal.
Immortality was conferred on Kripacharya by Lord Krishna through a blessing. Kripacharya was prioritized for the conference of immortality even above Dronacharya since Kripacharya demonstrated some great virtues like truth, righteousness and impartiality. Even under highly stressful conditions he was not prepared to compromise with his values and in this regard, he stands out as the noblest among men.
Kripacharya is blessed as immortal not just to maintain his physical deathlessness but to give life to all his sacred principles he followed. Kripacharya is prioritized over Dronacharya in reaching the position of immortality as he has not left his principles even at the time of diversity and stress.
The Adi Parva of the Mahabharata describes exactly who incarnated as each of the major characters in the Mahabharata. Concerning Kripacharya, guru of the Pandavas and Kauravas, it says [this][http://www.sacred-texts.com/hin/m01/m01068.htm]:
And, O king, that Brahman sage who, on earth, was known by the name of Kripa and was the embodiment of all manliness was born of the tribe of the Rudras.
Rudras are group of gods associated with Shiva and if he is pleased, he can even bestow immortality.
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