Murder, whether of oneself or another, is always a symptom of crossed signals in the brain. We are wired for survival, not self-destruction. I wonder if you're thinking about suicide the way the Catholic Church has taught, that anyone who suicides goes to hell. That is not a teaching of the Bible, but a theological assumption of Catholics because the victim didn't get the Last Rites. It's not a biblical teaching, however, but a RC Church teaching.

Suicide is a sin, for sure, because it's contrary to life to intentionally take a life. From what I interpret from your question, though, I don't think people who are mentally ill are held accountable for the acts they do "under the influence" of their unhealthy brains (in this particular illustration). We mourn the loss of Robin Williams, for sure, and the tragedies of all who take their own lives.

Is suicide still a sin if a mental illness drove you to kill yourself?

I don't mean that you kill yourself because you don't want to be mentally ill. I mean that you kill yourself because the mental illness prevents you from being rational enough to not kill yourself.

In case it isn't clear, I am specifically speaking of Robbin Williams taking his own life after being diagnosed with a mental illness that drastically changes ones's behavior. Normal Robin Williams would never off himself, but mentally ill Robin Williams had no defense against those thoughts.