A few points.

Firstly: The empire was not split in 2 in the 200s/300s. (Leaving aside Posthumus, that was more akin to a secession.)

In the late empire, there were multiple emperors. Not multiple empires. There was one Roman empire and various co-emperors ruling it. (Could be two, could be more.)

Now, this theoretical division of power broke down fairly regularly. Sometimes the co-emperors got into civil wars. In the 5th century the existence of different courts at Ravenna/Milan and Constantinople sometimes worked at cross-purposes and led to a more distinct separation.

But it should be remember that the final death-blow^* for the Western empire as a political entity was the failed attempt at reconquering Carthage and the destruction of the Roman fleet at Cape Bon in 468, just a few years before the traditional date for the fall of Rome. And that this expedition consisted of the combined forces of both sides of the Roman empire. They weren't very split.

Secondly: The reason for having multiple emperors was precisely to prevent disintegration of the empire. The crisis of the third century had seen 30 emperors ruling in a period of 50 years, with many attempted rebellions and uspurpations and civil wars besides. At one point whole multi-province regions of the empire split off. (That'd be Posthumus and his Gallic Empire I mentioned above.)

A lot of the changes we see in the later Roman empire were consequences of the problems of the crisis, or attempts to resolve these problems. (not always successfully)

To simplify the argument: if generals keep rebelling as soon as they command large enough armies, that means that pretty much the only way to use a large army is to have the emperor command it in person. And if there are multiple problems on multiple frontiers of the empire... that means you need multiple emperors to handle them. But that is very simplified, as I said. The longer explanation follows.

If it could have existed as one unified empire for all that time beforehand why couldnt it have continued so?

That is indeed the question. I think the answer is that the early empire did not need multiple emperors because the role of the emperor was less critical. In the early empire, there was surprisingly little governance. There was almost no bureaucracy, and large swathes of provincial territory were left more or less alone, save for tax demands. These regions were just governing themselves pretty much as they had done in pre-Roman times, at least on the level of cities and minor regions. There would be a Roman governor and a Roman garrison, to be sure. But outside of a few central cities, it would be rare for most locals to ever see a Roman.

Those governors, meanwhile, still often came from the Senatorial class as they had done in the Republic, and governed their provinces just as they had done in Republican times: by relying on their own resources, their own staff of friends, slaves, and freedmen, and private companies to handle things like supply and taxation. (The dreaded publicani, renowned for their extortionate practices, but fortunately for the provincials curtailed later in imperial times.)

This system worked surprisingly well... for a time. Rome's economic, military and cultural dominance was sufficient that the lack of direct control over the provinces didn't hurt much, and after Augustus the prestige of the Julio-Claudian dynasty was such that even the more resented emperors were merely replaced with a different family member after their assasination. When that dynasty ended, there was a civil war (the year of Three Emperors) but after that the subsequent emperors managed to arrange succession well enough that things stayed pretty stable.

But it did not last forever.

Firstly, after a few centuries of Roman rule, the provinces in the periphery were integrated more and more into the Roman world. More people thought of themselves as Roman, but that also meant they wanted a voice in Roman government, and it also meant they were far less dependent on Italy's economy for imports of luxury goods and participation in Roman culture, since they now had their own versions of both.

Secondly, peoples outside the borders of the Roman world had evolved in response to their interactions with Rome. The Romans were generally not very pleasant neighbours, as their many punitive expeditions across the Rhine and their many invasions of the Parthian empire can attest. This eventually led to Rome's neighbours becoming more organised and more militarised, and particularly when Rome was distracted by internal strife and civil war, and neglected to practice their divide-and-conquer manipulations, they would pounce. This meant that the border regions of the empire were becoming more fraught. Wars no longer only began because some Roman emperor wanted glory. This furthermore meant that people in the provinces were feeling less secure, and wanted the emperors to pay more attention to their safety.^**

Thirdly, the Roman political system ended up breaking down. Civil war was not new to Rome, and the civil wars of the 1st century B.C. had nearly ripped their empire apart. Augustus had stabilised things by winning the civil war and reigning for a long time, and also by removing military power from the hands of the old senatorial elite and keeping big commands in the hands of his family members and trusted generals. Unfortunately, a few centuries later, those senatorial elites were no longer that relevant, and the formerly less distinguished equestrian officers became more ambitious. Someone of relatively humble birth from a province far away from Rome could now end up being emperor. This vastly increased the number of men who could potentially seek the throne.

Combined with factors 1 and 2 this meant that it became far more likely that a moment of crisis on a border could lead to a local commander proclaiming himself emperor (or being proclaimed by his followers) because they wanted someone to deal with the problem and the actual emperor was far away and not responding. Only for the newly proclaimed emperor to march off to go fight a civil war to beat the sitting emperor. Which would then lead to more problems on the frontiers. Which would lead to more usurpers. Which leads to the vicious cycle we call the crisis of the third century.

(It was much broader than that. There was also economic instability caused by debasement of the coinage and some epidemics sweeping across the empire and the end of the Roman Warm period and who knows what else. And there were also regions that managed to escape all this trouble. It's hard to tell how it all ties together. But it was a bad time to be a Roman, at least in most parts of the empire.)

The Romans survived the crisis as a unified political entity, largely thanks to the efforts of a series of emperors that rose from the army of the Danube in the Balkans, known as the Barracks Emperors. They tried various things to stem the crisis, such as having central field armies commanded by the emperors themselves (much harder to rebel against) and also appointing co-emperors so they could deal with multiple problems at once. (Which, I should add, was not an entirely new thing. Even back in the 2nd century emperors like Marcus Aurelius had ruled with a co-emperor sometimes)

More broadly, what we see in the later empire, particularly from Diocletian onwards, is a strong trend towards centralisation and bureaucratisation.

The old, informal system of loose governance by the senatorial elite while most people in the provinces ran tended to their own affairs had broken down. The emperors replaced it with a much larger, more professional bureaucracy. (And a larger army and more professional officer class, split in a separate career track. No longer was one man expected to be both the chief civilian administrator and the general)

To prevent the risk of civil war and replace the informal systems that no longer existed, this system was much more centrally controlled by the emperors themselves. This meant that a late Roman emperor had many more overt levers of power than an early Roman one had. But it also meant that it had become a much bigger job, and that it was much harder to run things by just sitting in a palace in Rome. So they didn't. In the 4th and 5th centuries we often see emperors operating close to the frontiers in smaller regional capital cities, dealing with various crises.

And that's why having multiple emperors became less the exception than the rule. Governing the entire empire with one emperor alone was much less practical than it had been in the old system.

^*) If one believes there was such a thing as the fall of the Roman empire, at least. See Peter Heather The Fall of the Roman Empire for someone who does.

^**) Much of this argument and also much of the stuff below comes from Guy Halsal, barbarian migrations and the Roman West Though I've added bits and pieces from other places.