By the time Augustus ascended to the office of Imperator, the Senate was already weaker than it had been 100 years ago. In the interval, two people had challenged its authority and emerged victorious; Sulla, who had declared himself dictator for life in 81 or 82 B.C. (and bizarrely abdicated that position just a year later)^^1 , and Julius Caesar. Augustus, while solidifying his control over the Roman state, had the Senate give him many legal and military powers (including control over the wealthiest and most militarized provinces), and then set about reforming the governing body to better suit his needs. These reforms included reducing the size of the Senate from 900 to 600 members (though it was almost never full) and granting it all state judicial powers (which had been stripped from lower assemblies). During the early years of the Empire, the office of Emperor was actually a collection of titles, privileges, and authorities technically bestowed upon the imperial appointee by the Senate (though in practice the previous Emperor or the Praetorian Guard had the most influence when it came to choosing a new ruler). The emperor Tiberius increased the Senate’s power further with a declaration passing all electoral authority (the ability to appoint government officials) to the Senate, and Vespasian increased the body’s power in the city of Rome even further. During the next few centuries the Senate’s power variously waxed and waned, with some emperors, such as Hadrian and Domitian (Vespasian’s son), detesting the Senate with a burning passion (and in turn being detested by the Senate), and others expressing dismay that the Senate was no longer willing to aid them in their Imperial duties (I believe that Marcus Aurelius and/or Antoninus Pius did this at one point, but I can’t find any confirmation for that).
Diocletian, who reigned during the second half of the third century, severely curtailed the power of the Senate with a number of reforms that included the removal of most of the judicial and elective authority granted to it by the first emperors. However, many of those reforms were almost immediately reversed by Constantine, who also included the Equites in his Senatorial re-reforms. After his death, though, they began to gradually lose power, and by the collapse of the Western Empire they were a group of Italian land-holders with no authority, whose only real actions were futile attempts to reverse the spread of Christianity and return Rome to its pagan ways, and the occasional commission of treason (as individual Senators often sided with the many rebellious Germanic generals that came and went during the Western Empire’s death throes).
The end of the West did not spell the end of the Senate, though. It limped on through the fifth century, briefly gained influence during the Twenty Years’ Anarchy and the chaos of the 9th century, and then relapsed into practical insignificance. The office of Consul survived as the Greek hypatos in a much-diminished form until the 12th century, and afterwards is never mentioned again. The Senate itself fell further and further into irrelevancy, and by its end it was merely approving Imperial appointments. Its last recorded act is in 1204, with the appointment of Nikolas Kanabos as Emperor (though he never accepted the title). Three months later, the Crusaders sacked Constantinople.
Interestingly, the Senate in the West actually briefly survived the dissolution of the Roman state. The Senate was maintained as an advisory body by the Goths in Rome and Ravenna, and was restored a portion of its former glory after the Byzantine reconquest, often working closely with the Pope (in stark contrast to its pagan sentiments just a century before). However, it too began to decline and its last mentioned in an official document in 603, and likely did not long survive that date.
^^1 See responses
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