It’s often easy when explaining history to point to a specific date, but in actuality it’s really hard to point to an end date for the entire empire.

We can say that the Roman Empire fell in Britain when Constantine III stripped the island of military resources to fund his revolt in 407. Imperial control never returned after that. Another hard date can be applied to North Africa, with the fall of Carthage and the rest of Africa proconsularis in 439. These two regions definitively fell out of Roman control at pretty specific dates, and while Africa saw multiple attempts to recapture it, they all failed, leaving it to the Vandals until Belisarius.

As for the rest of the empire, there were multiple attempts by even the latest emperors to reconquer or at least reestablish control over territories connected by land to the heartland. Aetius and his ex-protogé Majorian are the best examples but not the only ones, just amongst the more successful.

Additionally, 476 is an arbitrary date. For instance, the last man to legally wear the purple died in 480, he might have been in exile but is there really a difference between a child puppet and an emperor in exile? Additionally, even if you ascribe to the view that the Byzantine empire was a fundamentally Greek imitation of Rome, it would be difficult to label the Eastern Roman Empire of 476 as non-Roman. So it’s hard to say that Rome fell, but easier to say that the Western half fell.

Plus, it’s important to remember that the vast majority of “barbarians” who settled in the former empire had been romanized through centuries along the frontier. As a result, they often coopted Roman sources or government and used Roman titles and laws to legitimate themselves. The best example of this is Ostrogothic Italy, where aside from being barred from serving in the army, life for Italian Romans largely continued as it was until the Byzantine reconquest. Something similar can be said of Southern France. Trade did not stop overnight, it slowly declined, as did cross empire communication, but not in any decisive way unless one was living in the periphery of the empire.

Ultimately I would say there is no one answer. We as historians can look back on events and mark them as turning points, such as Majorian’s failed naval invasion of Africa. But for many living in the empire it was a fairly slow process that went faster the farther you were from the core. However, even in Britain, a Romano-British culture survived for a while before being pushed West and gradually supplanted by the Saxons. It might not have been the Roman state but they were still people who saw themselves as Romans.