This is copied from my answer to a very similar question.

Interesting question. First, I think it’s worth addressing that both “end dates” and “start dates” for empires tend to be pretty arbitrary. Typically, there will still be someone calling themselves the emperor long after the empire has ceased to have any kind of real, political existence, and it’s up to the observer to decide when the empire “officially” ended. Nevertheless, there will usually be a consensus in favor of a specific date, or occasionally a couple of dates. And for the Byzantine Empire, as you noted, that date is 1453.

But why isn’t that date earlier? In 1204, as you point out, the city was sacked by Catholic Crusaders, who looted and burned indiscriminately, slaughtering many. The Crusaders established the Latin Empire of Constantinople, controlling a small part of Anatolia as well as the eastern coast of Greece, with Constantinople as its capital. This would seem like a pretty definitive “end”; the empire’s capital sacked, and in the hands of its enemies. And indeed, it certainly marked the end of the Byzantine Empire as a regional power. The empire of the Byzantines was effectively over, so why is this date not given for the end of the Byzantine Empire?

Well, while 1204 may have been the end of the Byzantines as a power, it was not the end of the Byzantines. Aristocrats fleeing the destruction in 1204 established several successor states, and the largest of these, the Empire of Nicaea, was able to drive out the Latins and reconquer Constantinople in 1261. Yes, this “restored” Byzantine Empire consisted only of western Anatolia and parts of Greece, and Constantinople was a shadow of its former self, but it nonetheless meant that Byzantium still had a real, political existence.

But to address your implied larger question, Why 1453? Why not 1326, when the city of Bursa in Anatolia fell? What about 1348, when Macedonia, Thessaly, and Epirus in Greece were lost? Or surely 1370, when the Ottomans controlled both Thrace and Bithynia, and thus all land surrounding Constantinople. From this point on, the Byzantines existed as an Ottoman tributary, controlling little more than the city of Constantinople itself. Surely that was the end of the Byzantine Empire. Or you might even make the argument that the last Byzantine-controlled territory wasn’t conquered until the Ottoman invasion of the Despotate of Morea in 1460, so that should be the “death date” of the Byzantines.

But the fall of the Byzantine Empire is dated to May 29, 1453, the day that the Ottomans conquered Constantinople. The significance of this event is not political or military, but psychological. To European Christians, Constantinople was still the imperial city; its rulers represented an unbroken chain back the glory days of Rome. The greatest city in Christendom, it had repelled wave after wave of Islamic attack, and its land walls had never been breached. To most, it was an invincible bulwark of Christian civilization. It’s capture, then, was a calamity of unimaginable proportion, for surely here was the death knell of Christianity. If the imperial city had fallen, how long before the rest of Europe was overrun?

To Muslims, the conquest was no less significant. In their conquest of Constantinople, the Ottomans saw themselves as the successors to Rome, capturing as they had the Roman capital (the Byzantine Empire thought of itself as Roman, and claimed to rule the Roman empire. Modern historians refer to it as the Byzantine Empire to avoid confusion). But it was more than that. The Ottomans had succeeded where the great Caliphs of the past had failed. The Prophet Mohammad himself had declared that whomever conquered Constantinople would be a great leader, at the head of a great army. Some Muslim scholars even saw the conquest as the sign of the coming of the Mahdi, a figure who appears in the hadith as a redeemer who will rid the world of evil at the end of days. While this obviously did not happen, it speaks to the symbolic important the city had.

Thus, the conquest of Constantinople is set as the end of the Byzantine Empire not because it was a crushing military defeat, or because it marked the end of the imperial system, or caused the collapse of the Byzantine political system. Rather, it is picked for its symbolic importance, representing as it does the decline of medieval Christian political power in the Eastern Europe and Anatolia, and the rise of the Islamic Renaissance empire.

TL/DR: The Byzantine Empire made something of a comeback after 1204, but the conquest of Constantinople in 1453 symbolized not only the end of the Byzantines, but of medieval Christian political power in the Near East.