I always have trouble with this because it seems to me to be so close to a meaningless question in the sense that if God wants something to stop being it'll stop, and if He wants it to go on being, it'll go on. So is it meaningful to talk about anything being intrinsically immortal?
Anyway, thanks for persisting with the thread.
God created man to his own imageIt would seem that mortality was acquired through sin, and so, the immortality was intrinsic and not conditional on God breathing new supply of life in.
(Genesis 1:27)God made not death, neither hath he pleasure in the destruction of the living
(Wisdom 1:13)by the envy of the devil, death came into the world
(Wisdom 2:24)sin, when it is completed, begetteth death.
(James 1:15)by one man sin entered into this world, and by sin death; and so death passed upon all men, in whom all have sinned.
(Romans 5:12)