The Eternal Reality of the Soul's Immortality

Sridhara Swami's Commentary
It may be argued that although it is certainly true that the Supreme Lord Krishna is not ever subject to birth and death being transcendental to the material manifestation what about the individual living entities who everyday are dying and being born. This is what is being answered in this verse. Even as the embodied living entity in the very same lifetime, possesses different physical bodies during different stages of life such as infancy, youth and old age; but always keeping the consciousness that one is the same individual despite these modifications presented in the form of the body. So it can be understood that on the destruction of the physical body the eternal soul is embodied in another physical body only due to the impressions one has accumulated in their subtle body and that the subtle body is real is observed at the birth of an infant who begins to suck the mothers breast immediately owing to past life impressions. The eternal soul does not perish when the physical body perishes; therefore the spiritually intelligent are not deluded by the birth or destruction of the body knowing that the eternal soul is not subject to birth or death.

Madhvacarya's Commentary
This verse confirms that the soul is distinct from the body but by it being distinct does not make it independent. Only when the physical body is seen changing through infancy, childhood, youth etc. can this separate distinctness be perceived and thus confirmed until the soul giving up its present body acquires a new body and in some rare cases a living entity can recollect their past lives.
The physical body is obviously not what has the experience of childhood, youth, etc as is evidenced when the body is dead. The body is just the container and when the soul has departed. The body has no further identification with the soul leading itself to experience that it is a human being or tiger or worm or whatever physical form it possessed as the case may be. But due to the fact that the soul remains within the physical body during deep sleep similar to the ego centered mind; it is possible to perceive the existence of the soul as an independent consciousness whereas the body is merely like a wooden box.
Ramanuja's Commentary
As the indwelling monitor in every individual body of all living entities the soul does not grieve at any modifications taking place in the physical bodies transition from infancy to youth to maturity to old age and that by this process it is not in any way affected. So similarly a living entity possessing spiritual intelligence will not lament at having to transition from one body to another body at the time of the modification known as death in this world because of the knowledge that the soul is always eternal.
The individual soul within the physical body of every individual living entity is eternal. Bound by the reactions of their own individual desires from time immemorial each individual soul incarnates into different bodies according to their individual karma. Then based solely on their past actions they are given a physical body which is their vehicle to evolve from bondage to liberation in the material existence by engaging in Vedic authorised activities appropriate to ones birth and qualification while but performing all activities selflessly without any motive for personal gain.
To those so conditioned as to be unable to be unattached to the fruits of their actions, the experiences of duality in pleasure and pain are unavoidable in as much that they are but the product of the material existence which come into contact with the senses as external objects. Hence one needs to tolerate all such dualities with perseverance during the undertaking of any and all activities.