"Temporary" vs "Eternal":
"Temporary" (may be sat-asat) means, something which keeps changing. It survives by repetition. "Eternal" (may be param akshara) means, with respect to which all these changes are happening. Both are permanent, but one is cyclic and other is constant.
A very over-simplistic analogy is:
-- In typical routine, you wake up every morning, get ready, go to work, come back, have dinner and sleep. Ideally these actions can repeat forever. All the above actions are "temporaries". They happen & vanish for a while, but again repeat. However, your home is "eternal", because with respect to your constant "home", everything happens.
To me, it appeared that jeevas are not eternal based on studying Gita. However I can be wrong. Below are some points which made me believe that.
During pralaya there is only 1 "nature" (bhAva in Sanskrit) which remains, when everything else is annihilated. There is absolutely no verse suggests that apart from this nature, the other jeevas would also continue to remain somewhere as separate identities.
I feel that the word "All" in various below verses is quite explicit and doesn't leave the slightest chance of separate existence of jeevas.
BG 8.18 — All become from unmanifested to manifested at the beginning of (Brahma's) day; At beginning of night, certainly (all are) destroyed into what is understood as unmanifest-able.
BG 8.19 — Like this, these elementary world (made of "5 elements" or "पञ्चभूत") certainly happens again and again; Upon arrival of night, it's destroyed; upon arrival of day it flourishes.
BG 8.20 — But there is an eternal Nature, which is beyond manifested & unmanifested; When all elementary world is destroyed, that remains.
BG 9.7 — O son of Kunti, all elementary entities enter my nature at end of cycle(Kalpa); Again I create them at the beginning of the cycle.
Possible source of confusion: "Soul"
Atma (BG 2.many) actually means "(true) Self" (Gita also uses I/me). It is also a representation of nirguna/nirAkAra Brahman (BG 8.20). Some call it "soul", as a synonymous. Now many people use "soul" to refer jeeva as well. However Atma and jeeva are not same. But because sometimes "soul" refers to both as a common English term, certain misunderstanding is created.
Atma ≠ Jeeva
This is clarified in wiki of Jeeva. Unfortunately, such articles also become source of confusion. They have cited BG 2.12, 2.16-21, 2.23-25, 2.30 to prove that Jeevas are eternal. However, all these verses describe Atma and doesn't have anything related to jeeva.
Here jeeva means something which differs between you and me. But it's same among your past births & my past births. As a matter of taste, some call it [individual] "consciousness" (chetanA).
Nirguna Brahman is eternal. Is jeeva "eternal" or "temporary"?
In other words, what happens to jeevas after pralaya (or towards end of Kalpa or Brahma's night)?
Note: Some answers suggest that, if "xyz" part (say mAyA) is removed from jeeva, then it's eternal. But if we remove something from jeeva then we are no longer referring jeeva. A specific quote which says jeeva (or equivalent) is eternal will be helpful.