"Infinity" in the temporary decaying material world means "eternity" eventually leads to "eternal reoccurrence" of all material combinations.

In other words, if you stick around long enough, the material universe will repeat itself.

The temporary material bodily vessels the jiva-souls are passengers in, are perishable and will decay over time forcing the jiva-soul to constantly change material bodies.

However, the individual "life" (jiva-soul) within each material bodily vessel is eternal and never decays as it moves from one material bodily vessel to another for infinity.

The jiva-souls have existed for "infinity" which means they are beginningless and endless and were NEVER created.

Bhagavad Gita As It Is "1983 correct edition", Chapter 2 text 20-

"For the soul there is neither birth nor death at any time. He has not come into being, does not come into being, and will not come into being. He is unborn, eternal, ever-existing and primeval. He is not slain when the body is slain." (BG Ch 2 text 20 "correct" edition)

Srila Prabhupada – "There are no new souls, new and old are due to this material body, but the jiva-soul is never born and never dies, so if there is no birth, how can there be new souls?" (Letter to Jagadisa dasa, 7/9/1970)

The implications of the "infinity" of individual "life" (jiva-soul) is mind blowing! 

Because in reality we never really die, therefore we (the eternal jiva-soul) is forced to change material bodily vessels because they eventually break down, wear out and cease to function.

Also, it's interesting to note that the combinations of material elements "over infinity" WILL lead to the "eternal reoccurrence" of all things material.

This is because eventually, over infinity, the combinations of material elements exhaust their "combinations"  and begin repeating their existence (the full circle) under the movement of time (past, present and future) that governs the temporary material manifestation.

This means over an enormous period of time, you WILL experience many material bodily forms by just being in the material world over "infinity."

However, the "real and only" cause of repeated birth and death that keeps the jiva-souls in the material world, is mistaken self-centred desires and simultaneously rejecting Krsna (God)

The only qualification for entering the spiritual world's "eternal presence of Krsna (God)" is by becoming "Krsna conscious," which means putting Krsna (God) first and in the centre by voluntarily doing everything for Him.

Krsna as His original form also never leaves Vṛndāvana in the spiritual world explained here.  

Srila Prabhupada - "Kṛṣṇa as His original childhood form NEVER leaves Vṛndāvana, all the forms of Kṛṣṇa that appear elsewhere are His Viṣṇu-tattva expansions."(BG As It Is Ch 10 text 37)

Srila Prabhupada - "The original Lord Kṛṣṇa never leaves Goloka Vṛndāvana. All the plenary expansions are one and the same Viṣṇu-tattva, and there is no difference in Their potency." (SB Canto 3 Ch 1 Text 34)

Srila Prabhupada - "Kṛṣṇa is the original Supreme Personality of Godhead, and Baladeva (Balarama) is Kṛṣṇa's immediate expansion. Because Kṛṣṇa NEVER leaves Vṛndāvana, all the forms of Kṛṣṇa that appear elsewhere are His expansions." (BG, As It Is Ch 10 Text 37)

Kṛṣṇa’s first expansion is Balarama, and from Balarama ALL Visnu-tattva expansions originate.

When the "original" Krsna wants to enter the material creation to perform His pastimes in the Vrindavana facsimile of the spiritual world, His Visnu-tattva expansion, coming from Balarāma, performs those Kṛṣṇa pastimes or lilas.

In other words, because the original Kṛṣṇa NEVER leaves Vṛndāvana, His Visnu-tattva expansion coming from Balarāma, plays the part of the original Kṛṣṇa in the material creation that includes killing demons there.