This is something I've debated with more than one person in the past, and while I acknowledge that perhaps I'm a little too attached to a principle of uncertainty and the unknowable, I'd say that the simplest observation is the most accurate:
The original human definition of life is based upon the assumption that life as it developed on Earth must provide some clue as to how all life in the universe develops. Furthermore, it is based on the assumption that all life operates on some common basic principles. This means that our science is biased because of the way in which we exist, which means that any conclusion which does not directly account for that possible bias has a high probability of being flawed. If science is a pursuit of absolute truth, then the only accurate observation is that we don't know anything for sure.
We as a species have apparently been 'in the making' for a limited amount of time. Our entire existence was dictated by the first cell that existed on this planet, unless life here has some extraterrestrial origin - in which case our history is merely longer, not more complex. The point is, all life on Earth exists because of the way in which life began on Earth. This does not permit the assumption that fundamental processes of the universe can't represent a form of 'life', but we operate on the assumption that it does. This is a mistake in our logic.
Fire is one of the fundamental processes of the universe - it can and does occur under specific circumstances, regardless of outside influence. That is not to say that outside influence has no effect on a natural process, only that the existence of such a process is undisturbed by exactly what occurs in our universe. We make more fire than might exist without us, but fire is always the same. For the religious among you, God could be considered THE fundamental process of the universe, and if something without the tangible properties we choose to associate with life is NOT life, then God is not alive. Does God need to be alive to be real? Apply this to any question and the only answer that is universally sound is that all we know is what we believe. As a species we are intelligent enough to conclude that it is unreasonable to define life by only the standards we know and understand, because we have been proven wrong time and time again. We choose to refer to this failure of logic as 'scientific progress', when in fact it is a method of creating new falsehoods which are immediately satisfactory, to be discarded when something more accurate is developed. If you need proof, consider the theory of relativity - we know it is obsolete and now we attempt to salvage what is still valid by assimilating it into more modern theories.
Life as we know it exists to exist. Reproduction is a method of genetic propogation. This ensures our survival as a species, and is reinforced by our drive to survive as individuals. Because each person wants to live, we all fight to the best of our ability to remain alive. The urge to reproduce exists fundamentally in all known organisms. Those who succeed are the best candidates to improve a species genetically. Because of intelligence and technology, the human race has moved away from these basic rules - rules which we invented based on observations of the life of a single planet. I don't think the definition of life is entirely bad, but I do think it fails to extrapolate upon itself. Why would an organism with no need for evolution continue to practice it? What is evolution? What would be the apex? And would we even know if we acheived it?
A basic process of the universe simply exists. It cannot evolve or devolve, it cannot change. It simply always has been and will be for as long as this universe exists. If fire is alive, it cannot die as a species because it can always occur, even if it never happens again in the history of all existence. If every human being dies, it's over. We're finished. Unless a precisely identical organism develops under precisely the same conditions for precisely the same amount of time, repeatedly until the end of time and space, 'the human race' will have a defined and finite period of time in which to exist. I think it's sufficient to say that the most probable scenario involves us dying off entirely with a thousand years or so. End of story. It would be lucky if there's a planet left for everything else by the time we go. We can't assume everything will follow the trend of Earth's 'natural order'.
To address the primary theory here...
The laws of thermodynamics are a popular citation in support of the concept of entropy as a reasoning that fire is not alive. Firstly, the laws of thermodynamics have been broken by natural processes of the universe: Energy cannot be created or destroyed. It has been observed that identical groups of matter and antimatter spontaneously generate throughout the universe, and annihilate each other to correct the imbalance of matter and energy in the universe. There are, however, situations where this process would be interfered with. A black hole is a one dimensional point of infinite density. It has sufficient gravitational pull to capture the fastest form of matter in the universe, light. This is not considering theoretical tachyons, which travel faster than light and thus move backwards through time as they move through space. I don't know how such a particle would be affected. As such, when a group of matter and antimatter occurs on the edge of a black hole, one half may occasionally be dragged in while the other escapes. This is an observable possibility, and implies that the laws of thermodynamics are not entirely consistent. They function for our purposes, but like the theory of relativity, they are apparently imperfect representations of the functioning of our universe. The details are unimportant. The fact is that our theories are imperfect and to assume truth based upon them guarantees some inaccuracy.
Secondly, and more importantly, the notion that life represents an entropic balance is questionable. The universe does indeed appear to be geared towards 'entropy', whatever that really is. However, what defines the 'organization' the makes DNA an exception to the rule? If waste heat from organisms composed of DNA nullifies the order of DNA, then we come out even anyway. However, I would argue that the 'organization' of matter into cellular, 'living' structures is no different from the creation of a star. These events occur because they CAN happen. If they can happen, and somewhere in the universe the proper conditions occur, it WILL happen. Stars burn out. Cells die when nourishment is no longer available. Both are conceptually the same, though one is more complex than the other. In the same way that organic life is propogated on our planet, the formation of galaxies and stars and planets and other various celestial bodies is propogated throughout the universe.
I don't think it's neccessary to get too involved in the question of defining sentience. We just don't know whether or not any given thing has thoughts or feelings. We don't even know what defines thought and feeling outside our own minds - all we can know is that we believe certain things that we assume to be truth. That the people around us share our feelings, or that they don't. That life is defined by a few simple rules, or that the universe is more complex than we can really understand. We don't know whether our experience of life is a figment of some greater imagination. We probably aren't the only lifeform in the universe, and we probably aren't the most developed. Whether the universe exists or not is entirely unknowable. Whether the natural processes of the universe are conscious in some recognizeable way can be determined, but consciousness can never be defined. If fire has thoughts, would it dismiss us as a mere 'occurence' of existence? Would we even be able to relate to the way in which some alien organism thinks?
In terms of fire, what this means is that we can only assume that fire could be alive, and leave it at that. We are probably never going to know. If we do, it will make no difference except to satisfy somebody's curiosity. That somebody will be dead within one hundred years, and the universe will continue on for however long its expansion dictates. Fire will always happen precisely the way it always did, and this is the best way for it to exist - it can't end because it has existed from the beginning. Assuming the universe exists. Assuming anybody but me exists. Being 'alive' is a very complicated thing.