In Julius Caesar, was Brutus responsible for his own downfall?

Brutus was responsible for his own downfall because he was naïve and did not listen to advice. 
The main reason that Brutus was responsible for his own downfall was that he did not listen to Cassius.  He never took anyone else’s advice on issues such as how best to assassinate Caesar or how to run the military campaign against Antony and Octavius.  Instead, he wanted to remain optimistic.  Since he did not, they failed.  He was naïve, and he paid the price. 
An example of this is when Brutus explains to Cassius that they should not kill Antony, because it will hurt their reputation with the Roman people. 

BRUTUS
Our course will seem too bloody, Caius Cassius,To cut the head off and then hack the limbs,Like wrath in death and envy afterwards;For Antony is but a limb of Caesar:Let us be sacrificers, but not butchers, Caius. (Act 2, Scene 1) 

Brutus believed that Antony’s only power was in his relationship to Caesar.  He underestimated Antony, but Cassius was concerned that Antony might cause trouble.  Cassius turned out to be right. 
To Brutus, image was more important than practicality.  Even though Cassius had been involved in the conspiracy longer than he had, he did not allow Cassius to have any sway over him and continually overruled his decisions in front of the other members of the group.  In addition to this decision, his decision to allow Antony to speak at Caesar’s funeral was especially disastrous, resulting in an uprising of public sentiment against the conspirators. 
Even when they have their own armies and are fighting the triumvirate, Brutus makes the same mistakes.  He argues with Cassius about going to Philippi, and overrules Cassius when he doesn’t want to go.  Philippi turns out to be a nightmare for them, and they both end up committing suicide there.  Antony and Octavius win and go on to rule Rome.