To my knowledge our spirit is eternal and does not nor will not decay or age. I believe the following scripture indicates that we shed that which is corruptible (our bodies) and our spirits which are made new when we are born again are eternal.
1Co 15:53 For this corruptible must put on incorruption, and this mortal must put on immortality.
1Co 15:54 So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory.
And:
New American Standard Bible (©1995)
Then we who are alive and remain will be caught up together with them in the clouds to meet the Lord in the air, and
so we shall always be with the Lord.King James Bible
Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and
so shall we ever be with the Lord.