Why did the conspirators fail in Julius Caesar?
The conspirators fail in Julius Caesar because they do not manage to take decisive control of popular opinion after their murder of Caesar. As Casca, one of the conspirators, notes, the crowd is extremely fickle and easily moved if its emotions are affected. For instance, regarding Caesar's fainting fit, Casca says:
When [Caesar] came to himself again, he said, if he had done or said any thing amiss, he desired their worships to think it was his infirmity. Three or four wenches, where I stood cried, “Alas, goodsoul!” and forgave him with all their hearts. But there's no heed to be taken of them; if Caesar had stabbed their mothers, they would have done no less. (Act I, Scene 2)
The conspirators know they must have popular approval -- this is why Cassius is so keen to get the support of Brutus. Again, Casca sums the matter up:
O, he [Brutus] sits high in all the people's hearts,
And that which would appear offense in us,
His countenance, like richest alchemy,
Will change to virtue and to worthiness. (Act I, Scene 3)
It is not in failing to recognize the need for popular approval, but in not knowing how to successfully get it, that the conspirators fail.
The most fatal manifestation of this failure is the conspirators' decision to not only leave Mark Antony alive, but to allow him to speak at Caesar's funeral. Cassius wishes to kill Antony:
I think it is not meet
Mark Antony, so well beloved of Caesar,
Should outlive Caesar. We shall find of him
A shrewd contriver; and you know his means,
If he improve them, may well stretch so far
As to annoy us all, which to prevent,
Let Antony and Caesar fall together. (Act II, Scene 1)
However, Brutus will not hear of it, thinking that this step is ignoble:
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. (Act II, Scene 1)
In the abstract, that might be a correct judgment, but the damage that the conspiracy might have taken from the ignoble assassination of Antony is probably much less than the damage the living Antony is able to do by whipping up the mob at Caesar's funeral.