As others have stated, I don't think that Zira was quite as insane before Scar's death, which in its turn made her into the pyschopath that we see in SP. I personally believe that she struggled with a lot of issues in her cubhood and maybe even adolescence, and she was likely very unstable even before Scar's arrival in her life and his death; I mean, to go as crazy as she did means that she had to have at least been slightly unstable in the beginning.
I just think that her obsession with Scar was reaching a new level when Scar's death happened. It pushed her over the edge, in my opinion.