How does Advaita Vedanta assert and prove the eternality of cognition of Non dual Atman?

Question

This article [1] says

Śāntarakṣita has however refuted the Upanishadic non-dualism in the Tattva Sangraha’ chapter 7, section 5. In his refutation of the Upanishadic view he has referred to the followers of the Upanishad as those who postulate that the âtmà is eternal, one and of the nature of knowledge/conciousness/ Jñànasvaråpa. Kamalaśīla has also commented on this view describing it as, “That is the âtmà is of the nature of one eternal consciousness / knowledge.” “The error in the view of these philosophies is a slight one – due only to the assertion of eternality of cognition.”

How can Advaita Vedanta prove eternal Atman as consciouness existing always? [1]: https://www.byomakusuma.org/VedantaVisAVisShentong.html

Answer 1

Prof Chandradhar Sharma on Critical Survey of Indian Philosophy, Page 312 writes,

A momentary idea can be neither self-luminous nor can it ideate itself. The reality of permanent self-luminous Self which is Pure Consciousness must be admitted. Vedanta criticizes only their momentary vijnanas and their view that external world is unreal because it is a projection of momentary consciousness as this view well smacks of subjectivism when consciousness is reduced to momentary ideas. Vedanta points out that the arguments which the Svatantra-Vijnänavädins advance against permanent consciousness are more applicable to their own momentary consciousness. To take an example, if bondage and liberation are impossible when conscious is treated as permanent they are more so when consciousness is taken as momentary. Vedänta accepts that Consciousness is Self-luminous and that it ultimately transcends the subject-object duality and the trinity of knowledge, knower and known and all the categories of the intellect. But from the empirical standpoint, stresses Vedänta, it is far better to describe Reality as Permanent and Pure Consciousness which is at once Pure Existence and Pure Bliss, than to call it momentary for whatever is momentary is miserable and self-contradictory. The momentary vijnäna can be neither self-luminous nor can it ideate itself. It requires the Pure Self which is Pure Consciousness to know it. Vedänta may well rejoin: The view of the Svatantra-Vijnänavädins is very much similar to Vedänta ; it contains very little error, its only fault is that it declares consciousness to be momentary.

In page 253, he continues,

The antecedent link in the causal series, says Shankara, cannot even be regarded as the efficient cause of the subsequent link because, according to the theory of momentariness, the preceding link ceases to exist when the subsequent link arises. If it is urged that the antecedent moment when fully developed (parinispannâvasthah) becomes the cause of the subsequent moment, it is untenable, because the assertion that a fully developed moment has a causal efficiency necessarily presupposes its connection with the second moment and this repudiates the theory of universal momentariness. Again, if it is urged (as is done by the Svatantra-Vijnänavädins) that the mere existence of the preceding moment means its causal efficiency (bhâva evâsya vyâpârah),this too is impossible, because no effect can arise without imbibing the nature of the cause and to admit this is to admit that the cause is permanent as it continues to exist in the effect and thus to throw overboard the doctrine of momentariness.