There are a few really obvious turning points, but the Crisis of the Third Century is the most obvious. It was the first time since Augustus the Pax Romana really faltered. The foundation of the Empire was the control of Mediterranean trade routes, and the Empire's legitimacy rested on its ability to ensure safe trade everywhere in the Med. The 3rd Century was the first time trade was seriously disrupted, and it was the first time regional military commanders declared themselves Emperors without having to secure Italy first. Without control of Italy's necessity to control the Empire, breakup was basically inevitable, even if barbarians hadn't been the ones to take control of the splinters of Western Rome. You also had a lot of knock-on effects like large landowners taking responsibility for neighboring small farmers. In many ways, Dominate Rome looked more like Medieval Europe than it looked like the Principate.
We've talked about the 3rd Century a few times, and I think the conclusion was that it was mostly preventable. Give the Empire access to a new gold supply to prevent debasement of coinage (a robust Sub-Saharan Africa trade is most obvious), and the other factors that led to the collapse can be fended off.
I'd say that preventing the 3rd Century Crisis solves a lot of internal problems and gives the Empire a better head-start to resist the chaos of the Migration Era. I mean, even as late as the 5th Century we have evidences that Rome could, with adequate leadership, muster the resources to face the invasions (Theodosius, Stilicho, Majorian, etc.), and so if we clock back to 200 C.E., when it still had a lot more of vigor, we surely improve its chances of survival in the long-run.
Also, I personally believe that the ultimate cause of the ruin of the empire (and that includes Byzantium all the way to after the 4th Crusade) were internal divisions, even more than foreign invasions. Nevertheless, if we could somehow
tweak through the centuries the various problems caused by the foreign invasions, we would, in any of these cases, give a "lease" of life to the Empire. For example, having the Germanic and Steppe peoples migrate in ways that they become less "concentrated" in certain regions, increasing the likelihood of a "breaking-in" like the Goths did in 370s, and creating less dangerous enemies in Persia and Africa. For example, people seem to agree that the Parthians presented a far lesser threat than the Sassanids, and without the likes of Shapur or (much later, I know) Khosrow, we also increase the chances of survival, so we can try the hardest to prevent a Sassanid-like Persian dynasty from ever taking power. The same applies, with the necessary changes, to the Germanic peoples, as well as the Slavs and Turks that comprised the "second-wave" of migrations during the 7th to 9th Centuries, and so forth.
In the very long-run scheme of things, considering all the possible chains of causality, from domestic issues (economic, social, political, cultural, religious, whatever), foreign ones (such as "barbarian" migrations and "civilized" threats), and macro-scale global ones (like a Hunnic, Seljuk or Mongol level scale of invasions, a continental-wide pandemic like the Justinian Plague or the Black Plague, and so forth), are a multitude of variables that influence on the survival of an empire so huge as the Roman, and thus we are reduced to a microscopical study of probabilities, with the objetive of reducing one or another of these chains of causalities to mitigate the negative effects on Roman survival.