592 said Pope Gregory I that it gives no Roman Senate anymore. Maybe after this date gives something called Senate, but this was not more than the city council of Rome.
The Popes used it occasionally after that.
It used the Popes, would be more accurate. Yes, it was reduced in power, but it still existed. The original Senate was no more than a "City Council of Rome," anyway. The Roman Senate was controlled by the Roman nobility. It had alot of power in the late 800's and 900's when the Roman nobility used the papacy as their chew toy; this was "The Age of Iron". It reappears (significantly) in the historic record during the period just before the "Babylonian Captivity" in Avignon. It was opposed to papal policies (their business interests were with Northern Italy, which was in conflict with the popes), and was the cause for a number of the rebellions and political problems that forced the popes to flee. After the popes left, it tried to convince them to come back to Rome, at various points by actually offering the popes (I think Clement in particular) a seat on the Roman Senate.