I have found the aion/aionios aidos question to be a difficult one to deal with, because English, Greek and Hebrew are very different languages.
I think it is a rational honest question when seekers ask, "If the fire isnt eternal- is the life eternal?"
Etymology is of limited use in the aion/aionios question(IMO) because they are translations of the older Hebrew word "olam". When we look for meaning in ancient words the goal is to understand what the speaker's thoughts were, in the words, in the time when they spoke. These speakers(Jesus, Paul, Peter, John, Luke) spoke Aramaic, a form of Hebrew, so the usage of olam in biblical Hebrew should explain the meanings of aion and aionios more than the etymology and usage among Greek contemporaries- they were largely alienated to Hebrew thought.
I would say this regarding "aionios pur" (age-during, or as some prefer, everlasting fire )- the fire IS everduring- but it only judges till you "bow the knee". Our God is a consuming fire. Jesus' eyes are as flames of fire in John's revelation. The eye is the light of the soul. When the fire has consumed all the adversaries we will rejoice in the fire and it will only make us shine. THE FIRE IS THE LIGHT OF GOD. IT IS THE DAY THAT BURNS THE DARKNESS. You only need fear the fire when there is something in you that needs burning.
The following scriptures show some insight into the nature of aionios fire.
Mat 3:10-12 And now also the axe is laid unto the root of the trees: therefore every tree which bringeth not forth good fruit is hewn down, and cast into the fire. I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire: Whose fan is in his hand, and he will throughly purge his floor, and gather his wheat into the garner; but he will burn up the chaff with unquenchable fire.
The fire here is for me as a believer. I am the wheat and I am the chaff. He will beat(sonship discipline) the seed until the chaff comes off. Then he will fan the chaff and it will separate from the wheat in the wind and He will gather the wheat. He will burn the chaff with unquencable fire. It will be unquenched until all the chaff is consumed. He is consuming the adversaries.
Mar 9:49-50 "For everyone will be salted with fire. "Salt is good; but if the salt becomes unsalty, with what will you make it salty again? Have salt in yourselves, and be at peace with one another."
The fire is the saltiness, it preserves the offerings in purity.
1Co 3:12-15 Now if any man builds on the foundation with gold, silver, precious stones, wood, hay, straw, each man's work will become evident; for the day will show it because it is to be revealed with fire, and the fire itself will test the quality of each man's work. If any man's work which he has built on it remains, he will receive a reward. If any man's work is burned up, he will suffer loss; but he himself will be saved, yet so as through fire.
The relationship between day and fire in the scriptures is extensive and a great study.
In my opinion, the real question is not so much wether the fire lasts forever- it is whether the torment and alienation last forever. My answer is emphatically NO. Otherwise Eph 1:5-10; Colossians 1:16-20; 1Cor.15:22-28; 1 Jn 2:2 and a ton of other scriptures are empty lies and the Bible is rubbish.
Col 1:16-20 For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers: all things were created by him, and for him: And he is before all things, and by him all things consist. And he is the head of the body, the church: who is the beginning, the firstborn from the dead; that in all things he might have the preeminence. For it pleased the Father that in him should all fulness dwell; And, having made peace through the blood of his cross, by him to reconcile all things unto himself; by him, I say, whether they be things in earth, or things in heaven.
The all things to be reconciled is defined in these verses clearly as all He ever created anywhere and all he rules over.
Eph 1:9-10 Having made known unto us the mystery of his will, according to his good pleasure which he hath purposed in himself: That in the dispensation of the fulness of times he might gather together in one all things in Christ, both which are in heaven, and which are on earth; even in him:
Eph 4:10 He that descended is the same also that ascended up far above all heavens, that he might fill all things.
Behold! I am making all things NEW!
We can't resolve all of this based on the Greek etymology of one word and maintain the integrity of the scriptures.
Here are some more scriptures that give evidence that our God is a consuming fire and to be near Him is too dwell in fire.
Isa 33:14 The sinners in Zion are afraid; fearfulness hath surprised the hypocrites. Who among us shall dwell with the devouring fire? who among us shall dwell with everlasting burnings?
Eze 28:14 Thou art the anointed cherub that covereth; and I have set thee so: thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire.
Eze 28:16 By the multitude of thy merchandise they have filled the midst of thee with violence, and thou hast sinned: therefore I will cast thee as profane out of the mountain of God: and I will destroy thee, O covering cherub, from the midst of the stones of fire.
Jas 5:3 Your gold and your silver have rusted; and their rust will be a witness against you and will consume your flesh like fire. It is in the last days that you have stored up your treasure!
1Pe 1:7 so that the proof of your faith, being more precious than gold which is perishable, even though tested by fire, may be found to result in praise and glory and honor at the revelation of Jesus Christ;
This, to me, is the revelation of the burning bush.
Our God will never cease to be a consuming fire. To dwell with Him is to have been consumed by, and filled with the awesome holy fire of His being and the light that shines from His burning glory! We are all passing through the fire every day. Some who believe will still pass through the fire in the Great Day, where the wood hay and stubble will be consumed. I believe the wicked will endure the penetrating light of His fiery day, revealing and consuming darkness until every knee shall bow and every tongue confess that Jesus is Lord.
1Co 15:28 And when all things shall be subdued unto him, then shall the Son also himself be subject unto him that put all things under him, that God may be all in all.
This God's ultimate intention and the reason for all He has done. He cannot be all in all in anyone who is alienated and in torment forever. So as I said before, I believe it is not about neverending torment, it is about all the enemies being subdued. That is a glorious subjugation into His love, and it is a fire every living being is already experiencing in one way or another even now.