In so many words, no. But if you can, that's quite an extraordinary claim and I'm sure the academic community worldwide would like to hear from you since they haven't figured it out yet. You make it sound rather obvious, I must say.
Let's look at the questoin in a little more detail, though. First, you argue that the legion was not very well suited to wiinning wars after about the first century AD while it was brilliant at it in the centurioes before. You could say the same thing about the army. I mean, look at the British Empire: The army could walk all over India in the 1790s and ruled the battlefields all over the world in 1850, and as late as 1900, while it had some problems, it still beat the Boers. Why was the army unsuited to holding on to the colonies in the 1950s and 1960s? I suspect the answer for the legion is similar.
The first assumption you make is that the conquests of the Republic were driven by Roman military technology. That is unlikely since Roman military technology was fairly easy to copy and was, in fact, widely copied. At least if you are talking about technology in the narrow sense. As a social technology, of course, Roman rule was extremely sophisticated and very hard to copy, but that ternds to be true for almost every instance of what we call 'social technology'. These things don't get invented, they evolve. Nobody quite agrees why the Roman Republic was able to defeat all comers for several centuries, but the best explanation seems to be a combination of a large recruitment reservoir, a social setting that rewarded participation in war, a warlike mindset that considered community honour an important value, an intensely competitive governing class that made war to acquire internal rank and status, and a target-rich environment structurally unprepared to oppose the political dynamic of the Roman system of empire-building. Being conquered by Rome was different from being conquered by other powers. Their alliance systems were more lasting and disloyalty was punished more fiercely. At the same time, they had the means to reward loyalty. Their government system could not be decapitated because their dedication to conquest was structural. You could not be a member of the Roman elite and not make war.
The technology of Roman warfare in the narrower sense was relatively simple and hardly superior to that of their opponents until the Principate. In fact, it seems to haver played a role in the halt of Rome's conquests that they ran out of technological and governmental equals. Their armies were of often questionable quality. That only changed with the first century BC.
At the same time, the first century BC brought the old Roman system to the limits of its capacity. You can have legitimate issues with P.A. Brunt's statistical analysis, but if you don't think he has a point, I'd like to hear youre rebuttal. The professionalisation of the military - a complete change in what the legion was - meant the liberation of much of the Roman manpower pool for nonmilitary tasks and the removal of internal conflict mweant that Aughustus could nonetheless still manage the largest territorial conquests in Rome's history. Soon afterwards, that dynamic begins to slow.
This slowing went hand in hand with serious recruitment shortfalls, a broad-based shift in elite culture and a broadening of the people on whose consent government depended. Military initiative on the part of governors and magistrates ceased to be a career booster and became a nonsurvival trait. Provincials could no longer be squeezed at will on the back of a Roman military based on its governing centre because the army's recruitment base shifted to the geographic periphery. At the hert of the Principate's initial ruiling ideology is the promise not to fight costly wars any more. It took the Roman Empire a long time to shake off this mindset.
Also, quite simply, the Roman model of conquest might have reached its limits. Roman rule dealt notoriously badly with decentralised enemies. It depended on a governing class to subject, suborn or replace. Outside the limits of the Empire, there were very few of those left.
Now, the Roman military changed greatly over all this time. The armies of the 3rd or 4th centuries were as alien to Caesar's as his would have been to the Pyrrhic Wars, maybe more so, given they completely abandoned the legion system even in name. Whether or not this change was technology-driven is questionable, but part of it very likely was (J.E. Lendon makes an extreme case, but it is not entirely unconvincing. A. Ferrill lays it out a little more impartially, but I don't quite buy his explanation either). The biggest problems that the Roman army faced throughout this phase don't seem to have been technological in nature - its technology was consistently at least as good, usually better than that of its opponents. Roman cavalry was excellent. Roman navies were top notch. Even its infantry continued to be good, though not, it appears, as good as it had been in the days of the Principate. The problem was the narrow recruitment base, increasing inability to sustain the effort required, and dependence on an overcomplex system to counter decentral and multiplying threats. Of course people have disagreed with this reading, but I think it's convincing. The Roman response of coopting potential enemies did not help in the long run.
Byzantium is a completely different matter again. Its military is based on that of the late Roman Empire, of course, because Byzantium really is the Roman Empire, but it changed its composition almost completely. It was able to militarily dominate its neighbours for a long time with a cavalry-centered, locally organised army (Maurice's Strategikon is good reading on this phase), but ultimately this structure did not prove the paacea it might have looked like. In the end, it wasn't the cannon that decided the issue. A city built for near a million people inhabited by maybe a tenth that number against one of the largest empires of its day is not a real contest. The Third Punic war must have looked similar - and the Carthaginians weren't beaten by a technologically more advanced foe, either.
Anyway, those are the aspects I consider most important, and if you can make a coherent narrative of technological maladaptiveness out of that, feel free.
