To my knowledge, the Greek doesn’t specify but the context seems to indicate to me that the impossibility relates to it being impossible for us, or possibly it being impossible for the person to repent in and of themselves. It’s not a reference at all to what is possible or impossible with God. Also, it seems that the writer is speaking Rhetorically and not Technically, speaking in generalities, not specifically. And it’s a side comment, not the main focus or goal of the passage. It’s a warning to not become so hard hearted that one must face the judgment/punishment of God. It’s a gentle rebuke through recognizing the extreme. Warning/punishment language is usually extreme, even hyperbole, overstatement, not technical/specific.
Is it significant that later on in the chapter he says:“But land that produces thorns and thistles is worthless and is in danger of being cursed. In the end it will be burned.”?
I notice that he says “in danger of being cursed”. Is “burned” presented as the alternative to being “cursed”? Or are they “cursed” and being “burned” is an example of this?
i think the if burning the land will make it more fertile, and yet burning could be seen as a punishment for the thorns and thistles…then could it be cursed to a punishment of being burnt, knowing that the burning is for the ultimate good of the field?
it would suck for the field, i suppose, but in the end it would recover and be the better for it in the end?
cursing of course doesn’t have to be permanent…Jesus “became a curse for us”…and yet is no way accursed now.
maybe our understanding of the word “curse” is a bit tainted by English folklore and myth
doesn’t it say, though, that it will not be cursed? That it well be in danger of being cursed is not the same as being cursed? Maybe I’m way off here…
good point…
so cursing could be theoretically different from the punishment of burning…
in danger of being cursed…in the end it will be burned…
nope, i don’t fully understand this!
Heb. 6: “7 When the ground soaks up the falling rain and bears a good crop for the farmer, it has God’s blessing. 8 But if a field bears thorns and thistles, it is useless. The farmer will soon condemn that field and burn it.”
The simile is not meant to teach specifics concerning punishment or judgment, but to inspire repentance. Even so, the field being condemned, cursed, and burned is in the context of reclaiming the ground.
A good point. The weeds are burned for a purpose.
Careful, I may be way off!
Unless the unrepentant one is represented by the destroyed thorns and thistles and not the ground!
Nope. But once again, the Greek word which some translate as “impossible” actually means “powerless”.
Note the primary meaning of the word from the online Bible Greek Lexicon:
102 αδυνατος adunatos ad-oo’-nat-os
from 1 (as a negative particle) and 1415; TDNT-2:284,186; adj
AV-impossible 6, impotent 1, could not do 1, weak 1, not possible 1; 10
- without strength, impotent, powerless, weakly, disabled
- unable to be done, impossible
“Impossible” is a derived secondary “meaning”, but in actuality not the meaning at all.
Do you think that this answers the question, though? Powerless for who?
The two grounds, fields are being compared, not the good crop vs thorns and thistles.
Fields bear fruit, like grain. Good fruit, or bad fruit - like thorns and thistles; are common themes in Christ’s messages and throughout the New Testament.
It would seem to me, there is far more case for a person being the “object which bears fruit” (a field) than the “fruit” itself. Unless God is purposefully giving birth to thorn-men and thistle-women, at which case one would have to rest blame upon the Lord for bearing bad fruit… 
The people in this particular passage must be the fields, or else the passage loses its consistency and goes off an on interpretive tangent.
I agree that the fields are intended to be metaphorically equivalent to people in the Hebrews passage. There is a very good parallel in 1 Corinthians 3: 9-15.
For we are God’s fellow workers; you are God’s field, God’s building. According to the grace of God which was given to me, like a wise master builder I laid a foundation, and another is building on it. But each man must be careful how he builds on it. For no man can lay a foundation other than the one which is laid, which is Jesus Christ. 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.
A metaphorical equivalence is made in verse 9 between God’s building or field and the people. The building or field represents people and some essential things about them, things they are trying to build or grow. These essential things could be their identities, their beliefs, and their resulting natures, for example.
These things about people will be revealed by testing on the day (i.e., judgment day) for soundness, and some people will be found wanting. Those found wanting will suffer loss. The use, in verse 15, of the word loss also suggests that it is people and such things as their identity, their beliefs, and their nature that are the buildings to be tested on judgment day. These are essential things that belong to people and stay with them. If these things are found wanting, the faulty parts will be removed and those affected will suffer loss. The word loss argues against the building as equivalent to our works, as some think, for how could works be called a loss to only some people when they die? Everyone’s works are lost to them at death. But people and their identities, beliefs, and nature are expected by Christians to live on. So, faulty parts of these things truly could be said to be a loss as a result of God’s judgment.
I just heard a lecture in which it was asserted that this verse is speaking of teachers that are building churches and not about all believers. Have you heard this?
Yes, I have heard of that interpretation.
But, I think the beginning of the chapter pretty well describes the people Paul is addressing, and they don’t appear to be teachers. For example, Paul speaks of the people as infants in Christ, those who were fed only milk, not solid food, which they weren’t ready to receive. The teachers appear to be Paul and Apollos, servants through whom the people believed.
Also there may be another clue in verse 9, “For we are God’s fellow workers; you are God’s field, God’s building.”
Note the different pronouns we and you. These different pronouns suggest that Paul is referring to two different groups, perhaps to himself and Apollos by the pronoun we (God’s fellow workers, meaning the teachers) and to the people by the pronoun you (God’s field, God’s building, meaning the students).
Yes.
Powerless for anyone who would attempt to restore such a one to repentance (including God). God is omnipotent, but having created mankind with free will just as He Himself possesses, He does not interfere with man’s free will. To do so would be to abrogate it. Thus as long as the person insists on going on his self-chosen path instead of the narrow path, there is no power on earth or in heaven which can restore him to repentence. He must choose for himself to repent.
aren’t the teachers building on the field, though?
Yes, at first. Paul refers to the fields earlier in the chapter.
**3:7 I planted, Apollos watered, but God was causing the growth.
3:9 Now he who plants and he who waters are one; but each will receive his own reward according to his own labor.**
So, at first, Paul and Apollos were working together to grow things in the fields. But then (Now) the people are the ones trying to grow things there.
Similarly with buildings, in verse 3:10, Paul calls himself one who laid the foundation of the building. But the people are building on it (note the clause another is building on it).
3:10 According to the grace of God which was given to me, like a wise master builder I laid a foundation, and another is building on it.
I’m kind of like that except on the opposite side. It’s either UR or nothing for me. 
I have just never been able to get my mind around ECT. I’ve tried a couple of times, but just can’t do it.