Attempting to prove that the "I" is eternal I think it's more interesting to view the idea of the eternity of the 'I' as an expression of something else—perhaps of an ontological need to keep oneself separated from historical time—rather than as a truth that can be assimilated into historical time:
There would be no separated being if the time of the One could fall into the time of the other. This is what was expressed, always negatively, by the idea of the eternity of the soul: the dead one's refusal to fall into the time of the other, the personal time free from common time. If the common time were to absorb the time of the "I" death would be the end. But if refusal to be purely and simply integrated into history would indicate the continuation of life after death or its preexistence prior to its beginning in terms of the time of the survivor, then commencement and end would in no wise have marked a separation that could be characterized as radical and a dimension that would be interiority. For this would still be to insert the interiority into the time of history, as though perenniality throughout a time common to the plurality—the totality—dominated the fact of separation. — Emmanuel Levinas, in Totality and Infinity
Surprisingly, Levinas also associates "the idea of the eternity of the soul" with
atheism, which he defines as "a position prior to both the negation and the affirmation of the divine." This is the reverse of what one might normally expect: usually, immortality is grounded by the existence of God, but here it is precisely the
abstention from the question of God's existence which keeps the soul separate and eternal.
In short, rather than try to 'prove' the eternity of the 'I', I think it is much more interesting to try to trace the idea back to its originary moments: what allowed this idea to begin and to continue, what 'needs' does it fulfill, and—assuming that Levinas is correct here, and that atheism, rather than religion, confers the idea—why is the idea so often proclaimed in religious contexts, and so often denounced in irreligious contexts? It's as if the idea is affirmed most strongly in the exact places it seems least to belong, and vice versa.