The last detailed mention of the Senate doing anything comes from the Greek historian Menander the Guardsman, who described two embassies sent to Constantinople to ask for reinforcement against Lombard incursions in the 570s. The Senate was further mentioned in a document describing the reception of an imperial icon in 603:

the icon of the . . . Augusti, Phocas and Leontia, came to Rome on the seventh day before the Kalends of May (25 April), and all the clergy and Senate acclaimed them in the Lateran in the Julian basilica: ‘Hear us, Christ! Life to Phocas, emperor, and to Leontia, empress.’ Then the most blessed and apostolic Pope Gregory ordered the icon itself to be deposited in the oratory of Saint Caesarius, inside the royal palace.

Curiously, Gregory the Great, the pope who received this icon, lamented the fall of the Senate in one of his homilies:

[C]ities have been destroyed, forts overturned, fields deserted, the earth emptied in solitude. . . . For since the Senate has failed, the people have perished, and the sufferings and groans of the few who remain are multiplied each day. Rome, now empty, is burning!

In another passage:

Rome herself once appeared to be the mistress of the world, yet you see what now remains of her . . . For where is the Senate? Where now are the people? Her bones have wasted away, her flesh has been consumed, every order of earthly dignity in her is extinct. The whole of it has been boiled dry. As for those of us who have remained, not few in number, each day we are still even now oppressed by swords and countless tribulations.

This is of course wild exaggeration, since Rome was neither empty nor burnt. It was a city that had lost much of its population compared to its golden age, but it remained an important settlement for the Roman Empire of the sixth and seventh centuries. Far from a doomsayer, modern scholars, such as Robert Markus, Matthew Dal Santo, and George Demacopoulos, see Gregory as very much a man of the empire, a loyal servant of Constantinople, and a tireless bishop who cared for his people. He was indeed a man with a grim apocalyptic mindset, but that did not prevent him from articulating a grand ecclesial vision or from discharging his duties effectively. In his sermons he aimed to urge the audience towards a better way of life - how better to encourage people towards the kingdom of God than to lament the miseries of life in the material world?

Now that the evidence for the Senate is out of the way, we can nonetheless presume that senatorial aristocrats remained and that they were still influential. Gregory himself was of this class and had served as the prefect of Rome before entering the monastic life. His contemporaries were no different, as some of the recipients of his letters were evidently of senatorial background, though I suppose that it is hard to tell whether they were of the eastern or western Senate. Anyway, 35 were identified as of the senatorial class by Tom Brown in his classic Gentlemen and Officers: Imperial Administration and Aristocratic Power in Byzantine Italy, A.D. 554-800 (1984). Finally, we can point to a later pope, Honorius (625-638), whose father was supposedly the consul Petronius; given his Latin name, it is very likely that this honorary consul was of the Senate as well.

But we have to be careful about distinguishing between the Senate as an institution and the senatorial class. The former was seemingly powerless, being only mentioned on official business three times after Justinian's reconquest, whilst the latter remained a substantial group. Beyond that we have to speculate, since the sources are not particularly helpful. For myself, I agree with Brown that the Gothic War utterly devastated the Italian aristocracy, lowering their wealth overall, but it also made it difficult for new aristocrats to enter the Senate - they needed to serve the imperial administration in some fashion in order to qualify. There were a limited number of positions available given Constantinople's prominence, so when combined with an influx of easterners in Italy, the Senate declined in significance. More mundanely, senatorial aristocrats also moved east to serve the regime there, which was perhaps a very sensible decision. The political centre had shifted to New Rome, so little wonder that an increasingly irrelevant body disappeared, so much so that we struggle to describe it in any detail, let alone how it occurred. The eastern senate of course remained an important body, which I described in more detail here.