That is a really good question, because the movement of the capital around the Empire is a great way to illustrate some of the wider changes that the Empire was undergoing.

Under the early Empire, Rome was truly the Empire's center. It was the Empire's most populous city and its richest, as well as the center of Italy, the richest provinces, citizens could go there to receive justice, and the emperor, Senate, and administration were all located there. It was not much of a military city, housing only a few thousand soldiers, but it was the center of military administration.

This began to change with the changing economics of the Empire. Over time, the provinces began to grow richer and eclipse Italy. Rome was still the richest city, but the economic difference was decreasing which lowered the importance of the city. I'm not entirely sure on population differences, but I would guess demographics were also changing in a similar manner. However, as much as economics were changing, it was strategic decisions that spurred the transferrals of the capital. The disasters of the Third Century Crisis (235-284) would draw the armies away from the frontiers, which provided an opportunity for the barbarian peoples outside the Empire to stage major raids across Roman borders. Combined with snowballing disease, increasing brigandage, a breakdown in trade, monetary debasement, and climate change, this was the largest disaster the Roman Empire had faced. In a move of desperation and necessity rather than design, the Roman army was forced to shift to a flexible, ‘elastic’-style of defence, where territorial integrity was only guaranteed in the immediate vicinity of the emperor and armies.

This system began to first appear under emperor Gallienus (253-268). Preceding him, Gallus (251-253) was still employing the Principate-style of creating a field army: when Aemilian (253) was marching on Rome, Gallus sent P. Licinius Valerianus, a senator, to requisition soldiers from the transalpine frontier to bring to Italy to bolster the troops already there. Most likely from his time on the Danube beginning in 254, Gallienus began to change this process by developing a stronger nucleus of soldiers that could form a permanent field army that could still be supported by reinforcements, but most importantly could also be effective independently.

In 260 Gallienus utilised this army to defend Italy from an invasion of Alemanni, which he defeated near Milan. Possibly in the face of this danger to Italy, he then established Milan as the headquarters for his new army under the command of Aureolus. This new army no longer carried full supplies, instead drawing from local resources, eventually creating dedicated depots roughly a day’s march apart from each other. Nor did they set up a fortified camp at the end of each march – as the army was now operating mostly in friendly Roman territory there was not such a danger of being ambushed in the night. These changes helped the army move more rapidly to respond to dangers, an important characteristic of a field army. Residing in Milan also placed this army in the perfect position to defend Italy against a possible invasion from Gaul by Postumus, as well as threaten him with the possibility of attack.

Thus over the duration of the Third Century Crisis the Roman emperors had basically abandoned Rome as the strategic centre of the Empire. Diocletian's reforms cemented this change when he created the Tetrarchy - two senior emperors and two junior emperors, each controlling a quarter of the Empire from their own capitals. These were Nicomedia, Sirmium, Milan, and Trier. All these locations were chosen for their defensively strategic placement, and throughout the fourth century the capital was a much looser and changing place than we think of today. The Senates (Constantine having created a second Senate) were still in Rome and Constantinople, the two most important cities, but the emperors now only visited those cities and never stayed long. Furthermore, the emperors were now even more important as they were escorted by a large army and most of the Empire's administration. Some of the other important cities were the emperors would reside included Antioch, Cologne, Rheims, and Paris.

The final development in the Romans' choice of capital came about as a result of the child-emperor phenomenon. In 395, Emperor Theodosius died and left the Empire to be inherited by his two sons, Honorius (eleven years old) and Arcadius (eighteen years old). These two emperors and their successors were dominated by administrative and military officials who hoped to use them as puppet emperors, even when they were of age. Thus, these emperors were essentially confined to their capitals - in the east, this was Constantinople, and in the west, this initially continued to be Milan but it was soon changed to Ravenna. Both these cities were exceptionally easy to defend, both being on the water so they could be supplied in the case of a siege, and both being well defended from the land-side. Ravenna was poorly placed to defend Italy from invasion, while Constantinople was perfectly placed to defend Anatolia from any invasions from the European side and this is often used to help explain why the eastern Empire survived the fifth century while the western Empire fell.