Several reasons. Although it's easy to look back at the historic size of early Imperial Rome (a million plus people at a time when no other city passed 300,000) and wonder why its population has (seemingly) grown so slowly, a lot of different things have happened to the city in the last two thousand years that few people are cognizant of.

First, it's important to understand from the outset that city of Rome was, at its early imperial height, an artificially inflated city. In the ancient world, city size was strictly limited by the amount of local fresh water and arable farm land. If the city was a major governmental center or trade hub, additional food might be shipped to it from further away, so population sizes might vary between 20,000 and 50,000 depending on these factors, but we hear of few ancient cities above this range. The few we do hear of - Antioch Alexandria, Carthage, etc... and of course Rome and later Constantinople - were THE major cities in their region of the empire. Alexandria and Antioch both lay on major trade routes and were the administrative centers for Rome's richest provinces, Carthage was another major provincial capital in a wealthy province.

But even among this top tier, none of them could rival Rome in population. Why? One factor was that the central government gave out free food (originally just grains, but later baked bread, some meat, some cheese, some wine, and olive oil too) to the poor. This grain dole was paid for by the state at great expense, and shipped in huge quantities from Egypt, Sicily, and North Africa, which had grain to spare. Depending on the period, between ten and twenty five percent of the people in the city benefited from this free grain, even if only tangentially (not having to provide food for your poor relatives makes it much easier to feed yourself.) another factor, almost as important, was that Rome was both absolutely filthy rich, on a scale no other city would be until 19th Century London, and, in the first two centuries CE, the center of all political gravity west of the Himalayas. Hundreds of thousands of people came to Rome in for the opportunities that its money and power provided. Hundreds of thousands more were brought there unwillingly as slaves.

All of these factors combined to artificially inflate Rome's population well beyond the normal limitations for cities in the ancient world.

Now, as time passed, the center of political gravity in the Empire and its hinterlands increasingly shifted away from the people and institutions of the city of Rome itself to the individual person of the Emperor and/or his court. Although the money continued to pour into Rome, by the late Third Century political power was now focused on the Emperors, who tended to rule far from Rome. This had an effect on the city population: by 400 CE, only 800,000 people remained in Rome, compared to a first and second century population that some estimates have put at between one and one point two million. Many of the emigrants belonged to or had aspirations of serving the central government in some way, and could no longer find what they sought in Rome. As power withdrew from Rome, its artificially inflated population slowly deflated.

But it was the fifth and sixth centuries that really decimated the city's population. Rome was sacked - to varying degrees of brutality - THREE times in the early-mid Fifth Century, and as the Western Roman empire began to dissolve (between the 430s and 460s) it could no longer reliably secure or pay for the free food it had once provided its inhabitants. Between these fifth century factors, the population plummeted.

Some estimates suggest that only 200,000 people remained in Rome by the beginning of the sixth century, a number roughly on par with what we see from Alexandria and Antioch, suggesting that now that both Imperial power and free food supply had been removed from the city, it had shrunk back down to a size typical of a wealthy regional capital.

The population may have recovered somewhat in the first three decades of the sixth century. Theodoric, who ruled Italy nominally as a viceregent, or junior Imperial partner of the Roman Emperors in Constantinople (the Imperial cloak and diadem were sent to him and he was allowed to mint coins in his image, although he appears to have assumed the humbler visage of an early Imperial princeps instead of the stylings of the dominus employed by his more recent predecessors [probably as a means of showing his nominal submission to the Senior Emperor in Constantinople, even if he was more or less independent in real political and military terms], his heir was adopted by the Emperor in the East and made consul, and he was referred to as 'Forever Augustus' in one particularly sycophantic Senatorial inscription) seems to have restored the grain dole, possibly with supply from Sicily, (now that the population had shrunk significantly, Sicily could easily satisfy the city's hunger.) The population may have climbed back to 300,000 by the end of Theodoric's rule.

However the mid-Sixth century not only halted demographic recovery, but saw its near total collapse. The devastating Romano-Gothic wars of the 530s-550s saw the decimation of nearly every major urban center in Italy, including Rome. The grain dole ended for good sometime during this period. The aqueducts were cut. The city was seiged, sacked, and changed hands repeatedly. Moreover, the Justinianic plague that arrived in the late 530s killed roughly half of the people wherever it went. By the 550s, estimates put Rome's population at less than 30,000.

Rome never really recovered after that, and there were no serious attempts in the medieval, Renaissance, or Early Modern periods to revive it on anything like its former scale. For centuries after Justinian's wars, Rome, along with Ravenna, Naples, and a few other strips of Italian territory held by the East Romans, was largely ignored. There no serious attempts to revitalize it, the aqueducts were not restored, and the free food supply was not reinstated.

The city remained at roughly the same size (between 30 and 90k, depending on the estimate) until the 1800s, when the growing material prosperity, industrialization, and improvement of farming techniques allowed for city populations to begin expanding at exponential rates. Although throughout the medieval, Renaissance, and Early Modern periods the city remained the center of Christendom in Western Europe, and thus an important financial center, the money poured into the church does not appear to have raised local prosperity and incentivized migration the way that the liquidity of wealth in the Imperial period did.

So in answer to your question, Rome has only truly begun growing again in the last 200 years, from a modest 50,000~ to the 2,000,000+ of today roughly on par with other Industrial Era urbanization booms. But unlike Great Britain and North America, Italy has not become a major power player in most of the last two centuries' worth of politics, and has not benefited from the influx of wealth concentrated in the great cities of major powers: thus it has grown only moderately in comparison to, say London, New York, etc.