God is beyond our perception of time, so this question is almost meaningless. God is a master of time, not a slave of it.
Time is one aspect of God. Both time and space are a way for God to give form to his creation. There are a myriad of ways for one aspect of God to relate to another, and through such relations God creates physical form.
If something is eternal, then it partially defeats the purpose of time. Through time we recognize change, and it is change that allows the breath of God to permeate the universe. If something changes into itself, then it seems to us if it is unchanging, but that is not the case. For example, the human body changes completely every seven years, regardless of if we notice the changes that happen every moment or not.
If something changes into itself, we can say that thing is 'stable'. If change is erratic, then it is 'unstable'. For humans, too much of the same can become a form of prison, since if we are limited in change we are limited in exercising our free will. In a way, being eternal could be a negative thing too.
An eternity can be only a moment for God. Although particular forms or aspects of God are not eternal, God is eternal in the sense that God is present as long as the time of the world exists. What we humans tend to forget is that time is a unified whole too. Chopping up time into seconds, minutes, days, centuries etc. is just a human way of looking at things and not the basic reality of time itself. Eternity, as an infinite series of moments, simply doesn't exist.