Let's start from the beginning with what we know - what we're told.

There are two spirits in play that are of interest regarding created man and his potential for (intended) eternal life.

 1. the spirit in man
 2. The holy spirit that God gives to those He chooses (the 'choosing' is not important here)

> Romans 8:16 The Spirit (of God) itself bears witness with our spirit, that we
> are the children of God.
> 
> Ecclesiastes 3:21 the spirit of man that goes upward, and
> the spirit of the beast that goes downward to the earth?

Imparting an understanding that nothing but mankind has a life potential past the present fleshly life of death. (death for two reasons - we are physical and subject to daily decay, and spiritually dead because of Adam's sin and resultant corruption of all men)

When we die in this age, we remain dead until we are raised - no one is going to heaven. 'No one has ascended into heaven except he who descended from heaven, the Son of Man', John 3:13

The spirit that God has placed in us returns to Him at death - Luke 23:46 Father, into Your hands I commit My Spirit (Jesus dying). Eccl 3:21 again. Acts 7:59 Stephen dying. This isn't the holy spirit.

> Hebrews 12:23 And to the assembly of the firstborn who are enrolled in
> heaven, and to God, the judge of all, and to the spirits of the
> righteous made perfect

Now we see reference to the spirits made perfect - believers whose spirits are sanctified etc and made acceptable to God through Christ. So these human spirits *were not righteous* - but sinful. 

And we go back to the start again...

> Romans 8:16 The Spirit (of God) itself bears witness with our spirit, that we
> are the children of God.

God determines that we are perfected because there is harmony between His spirit and ours - both are of God, but only one is made subject to our will and corrupted environment - that of the devil.

This human spirit is the same as Jesus' spirit when he fought to bring his will into subjection with the Father's will when facing imminent horrific suffering and eventual death on the cross.

We see by Paul's hand the choice to commit a man to 'death' in this age, that his spirit might be saved/perfected in the next. If the man was to continue fleeing God's will he would find it harder (perhaps by Paul's thinking, impossible) to return when given the chance.

> 1 Corinthians 5:5 You are to deliver this man to Satan for the
> destruction of the flesh, so that his spirit may be saved in the day
> of the Lord.

Again we see the contrast of the man's spirit with inherent free-will component - able to rebel and sin, against the spirit of God that would transform him eventually to Himself - being saved.

**So, the spirit in man is of God, but by no means divine** - NOT holy by any means. Just as the spirit in animals is not holy either - only difference is they are not being saved or redeemed. 

Based on this assessment, there is no immortal component to the person - they die and remain so until a resurrection - their spirit goes back to the God who gave it. 

If God has been at work in us Phil 2:13, we will be raised in the 1st resurrection to eternal life - joining with Jesus.