https://www.speakingtree.in/blog/why-is-kripacharya-immortal
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.
https://www.knowswhy.com/why-is-kripacharya-immortal/
This website also says similar thing.
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.
https://www.sacred-texts.com/hin/m10/m10017.htm
If Mahadeva be gratified, he can bestow even immortality.