Brutus' downfall is perhaps one of Shakespeare's most tragic, as it comes as a result of the qualities that also make Brutus most heroic: his deep sense of honor and nobility. Unlike the other conspirators, Brutus does not kill Caesar because he is jealous of the man's swift rise to power; rather, Brutus joins the assassins in order to protect Rome's representative republic and to guard the common Roman plebeians from an authoritarian dictatorship. Since he joins the conspiracy with such honorable intentions, he also assumes that others will abide by the same code of honor, and so he allows Mark Antony to give a speech at Caesar's funeral, and the cunning politician uses this time as an opportunity to convince the mob to turn against the conspirators. Thus, Brutus' downfall is caused by the same innate sense of honor that also makes him a successful leader in the first place.
But that's not all; if we're talking about Brutus' downfall, it's worth mentioning that, while Brutus is highly concerned with protecting the political freedoms of the plebeians, the common Romans are quick to turn on him. Indeed, Antony's funeral speech is enough to turn public opinion against Brutus and his companions, even though they quite recently believed that Brutus was "an honorable man" and that his actions were just. As such, Shakespeare explores the fickle and unjust nature of mob mentality, showing how it lacks reason and rationality and can be swayed by someone clever enough to manipulate it. If Brutus' downfall is already tragic, then his misguided faith in the "mob" of Rome merely serves to pour salt in the wound.