Super soul (God) and Jivatman (individual soul) are both immortal. However our physical, material bodies are not immortal. In fact nothing in material world is immortal nor it is supposed to be. And once the material universes end the new cycle of creation will begin. There is no permanent end in the Eternal Religion. Cycles of creation and dissolution of material universes will go on. At the time of dissolution of material universes those souls are still not disturbed who have already attained moksha because they are already in Golok Vrindavan or Vainkunth, the abode of God. And when material universes are annihilated the abode of Lord is still untouched and unchanged and eternally blissful as Krishna says:
"When Brahma's day is manifest, this multitude of living entities comes into being, and at the arrival of Brahma's night they are all annihilated." - Bhagwad Gita (chapter 8, verse 18)
"Again and again the day comes, and this host of beings is active; and again the night falls, O Partha, and they are helplessly dissolved." - Bhagwad Gita (chapter 8, verse 19)
"Yet there is another nature, which is eternal and is transcendental to this manifested and unmanifested matter. It is supreme and is never annihilated. When all in this universe is annihilated, that part remains as it is." - Bhagwad Gita (chapter 8, verse 20)
"That supreme abode is called unmanifested and infallible, and it is the supreme destination. When one goes there, he never comes back. That is My supreme abode."
- Bhagwad Gita (chapter 8, verse 21)
Now question arises what happens to those souls at the time of dissolution of material universes who have not attained liberation from material existence? Such souls enter God in deep sleep but obviously their material bodies are dissolved and awakened again when new cycle of creation begins in new material bodies. And one more thing is when individual souls enter God they don't lose their existence. They remain in unmanifested and impersonal God but maintain their individuality.
So in short the Super Soul and individual soul both are immortal.