Problem: Generals are always ready to fight the last war. In TOL's case, they had 1000 years and yet they try to use the same tactic that they know didn't work last time. WHY?
Incompetence
TOL is generally shown as fairly incompetent in Kingdom Come. However, these have to be exceptions in the overall plot: much like Carpathia, whose ascent to power happens in a time skip, TOL simply has to get a lot done in the 900 years of the Millennial Kingdom that we are not shown. This is probably because the authors don't want to show us their bad guys winning, and because every event in every book is shown from the perspective of a Christian caracter (for a series that has God as the protagonist, interestingly, we never get omniscient perspective, instead dealing with this or that main character traveling around to witness this or that event. Even the Last Battle is shown through Rayford's supernaturally enhanced but otherwise failing eyesight; we have no way to tell whether Rayford is a reliable narrator, and there are many hints in the earlier books that he isn't.
One interesting note to make is at the end of chapter 32, after the main time-skip, in which we see how decrepit the Natural characters are with about 200 years still to go in the Millennium. There, TOL is shown as having managed to revert some of the changes that God enacted upon the Holy Land after the Appearing: Millennial Israel is shown as a green, fertile land... except at the end, when Rayford is old and complains of feeling chilly even in the desert heat. This is significant: since Rayford is at COT's main campus in Israel, which is close enough to the Ultimate Temple that it's within walking distance, it means that the desert has reclaimed most if not all of the Holy Land. This is unlikely to happen naturally since the ecosystem is Divinely managed... so we're looking at an active terraforming program, and there's only one faction that would bring the desert to Israel, perhaps as a show of power, or perhaps as a test for other plans: The Other Light. Certainly, the fact that they have brought the desert back to the Holy Land, in specific defiance of Divine will, appears prominently in their propaganda.
There's also the simple fact that TOL goes from a fringe group to an industrial and military giant over time: TOL have enough industrial might to build an enormous army that operates at WW2 levels of technology (we are told that they have warships and missile launchers, although interestingly, they lack an air force), enough scientific might to perform hostile terraforming against Israel, and enough political might to grow their ranks from dozens to billions despite the obvious handicap of a much shortened lifespan. So, we must rule out incompetence: TOL may be misguided, but they have skills. In fact, the authors go out of their way to pointing out how Kenny Williams makes sure that TOL shifts their recruiting priorities from "dopers and alkies" to intellectually capable and skilled people!
Insanity
It's entirely possible that people who join The Other Light, The Only Light or any of the other factions are either insane or go insane by the time they realize that they have no hope of winning; the definition of insanity is doing the same thing over and over and expecting a different outcome, and this fits what's going on to a tee.
The problem is that this sort of insanity precludes being able to keep to a plan for many generations, especially if that plan involves tanks, missile launchers, and warships. We know that there are no wars or even rumors of wars until the closing years of the Millennium, which means that any TOL civil wars would have to happen right before the Last Battle, or else happen in a Dune-esque "war of assassins" fashion that goes largely undetected by the outside world.
Insane people in charge of warfighting equipment don't upgrade, maintain, and train with that equipment for centuries without incidents. So, we have to rule out insanity (although it's very likely that TOL has had a Caligula or two at its helm during its 950-year history).
Inevitability
God is just puppeteering everybody, or at least a significant part of the population (the Last Army is supposed to be a billion strong; if you consider the amount of support personnel a modern army must have, this means that at minimum, at the end of the Millennium Christians are once again in the minority).
This basically turns Kingdom Come into a Lovecraftian cosmic horror story, in which nobody has any choice - being Glorified maps eerily well to being eaten first... This is possibly what the authors believe, but there is really no way to analyse this scenario without succumbing to madness or solipsism. We cannot strictly speaking rule out inevitability, but inevitability reduces the whole book (if not the whole series) to us watching God play with army men, by Himself.
This is more extreme than Calvinism: it essentially accuses God of solipsism, and implies that maybe He doesn't have any choice either. I doubt that this was the authors' intention.
Innovation
TOL had 1000 years to come up with a better solution, and their stated recruitment doctrine is to poach the best and brightest. I propose a solution in "Countdown": many if not most members of the Last Army are already damned to start with. They have accepted their ultimate fate, and are sacrificing themselves for the greater good so that another plan may be enacted.
Interestingly, TOL's great army is shown to feature ground and naval forces, but no airplanes as they advance towards the Temple. Could they simply be elsewhere? The all-consuming firestorm at the Last Battle is shown to move fairly slowly, slow enough for a modern aircraft or even a 1950s military jet to easily avoid. What if Rayford was Raptured just in time to avoid seeing the Ultimate Temple carpet-bombed? This is possible, but there's simply nothing in the text that hints at it.
Maybe there is a simpler explanation: the Last Army is itself nothing but a huge military ruse. Now, what would be the point of applying maskirovka (military deception) against an enemy who is either omniscient, or close enough to omniscient that it makes no practical difference? Simple. The power of God may be limitless, but God has limited Himself by giving Himself a script to follow, and then following it to the letter - we see this in the other Left Behind books, where very often things happen simply because they have to happen according to Revelation or the book of Daniel. It is written that Israel will become prosperous when the desert blooms, and so this happens, regardless of the obvious political and economic facts about the region. And so on.
TOL strategists likely figure out that, should they break from the prophetic timeline, God would simply exercise His omnipotence and do something like resetting the universe, or sending everyone to Hell instantly, or who knows what else. Therefore, unlike CATS in my AU, they put effort into keeping things "on rails" as a way to effectively limiting the amount of force that God is going to bring to the table. They know that they have to lose the Last Battle in order to win the war.
How can they do this? TOL is definitely playing for all the marbles here: the very survival of humanity is at stake here. An obvious exit strategy would be to send colony spaceships to settle on other planets, or even nearby stars by use of a generation ship - an organization that can arm a billion soldiers in 900 years can definitely do a Moon shot or a manned Mars mission. The question then becomes, how far away is far enough? "New Earth and new Heaven" in Kingdom Come specifically refer to the planet and to the sky canopy above it; the rest of the cosmos is left alone. That said, Jesus' rolling wall of fire that destroys the Last Army looks a fair amount like a nova or gamma ray burst (the atmosphere is lit on fire by secondary radiation) coming from the Sun, so an interstellar escape may be the only option unless TOL has managed to build "fallout shelters" that can hide behind Jupiter or Saturn's magnetic fields.
The Omega chronicle (which you can read at http：／／www．f3．to／omega／ ) tackles some of these topics. In it, to ensure continuity of operations given their operatives' comparatively short lifespan, TOL create an AI (in the modern sense, not in the HAL 9000 sense) to handle day to day business. The AI's expert system is quickly taken over by a group of sysadmins with a variety of agendas: despite the infighting, TOL becomes able to enact a strategy that gives God everything He wants while succeeding in preserving Humanity beyond the White Throne judgement.
The solution presented there is by all means not the only one: the chronicle has been written in the form of a game specifically to encourage others to be creative about this problem.
As part of the research for my fanfiction, I have recently been able to interview creationist evangelist Kent Hovind, the author of the canopy theory that is used in Kingdom Come to explain why there is no night. In "Cendrillon", I postulate that the canopy would have a lower layer of water, an upper layer of ice, and exist at approximately 70 kilometers up; Mr. Hovind said that he envisions the canopy as being significantly lower on top of the atmosphere (16km or so) and composed of supercooled vitrified ice about 7~10 centimeters in thickness. This would require a significant rewrite in the stories of both Cendrillon and the Omega, but if anything, it would make their job simpler: no water layer means no need to make the capsule waterproof, and a lower canopy height means both that a smaller rocket is required to reach it and that space missions leaving from the top of the canopy could make more efficient use of the Hoberth effect. Cendrillon and the Omega have, in fact, been "playing on hard mode" this entire time!
My whole point is that Kingdom Come does not necessarily have to be the story of Humanity's struggle ending with a bang and then a whimper: even taking Rayford's point of view in the last chapter as what happens, rather than what he perceives as he experiences the second Rapture (after having had his sight and mental faculties supernaturally restored following at least two centuries of decrepitude... or so he thinks, anyway) there is plenty of room for a part of Humanity to have survived, out there in the endless black.
In conclusion... as much as the text has a lot in common with a Cosmic Horror story, there is plenty of room for hope for Humanity in "Left Behind".