Couldn't Niniel and Turin work this out?

[Ibrîniðilpathânezel]

Just to toss in my two cents, I would venture to say that a key element in suicide, as Tolkien presents it, is the matter of pride and/or despair that Gandalf mentions. Both Nienor and Denethor killed themselves in despair. Éowyn actively sought death (and kept on seeking it) in despair, until her despair was healed. I get a feeling that Faramir felt more frustration than despair, that it seemed that nothing he could do, short of dying, would win his father's approval.

But in Tolkien's world, one would have a hard time always defining the willful ending of one's life as the "sin" of suicide. The Númenoreans, blessed with long lives, were supposed to surrender the gift of life and accept the Gift of death when the time came. Evil often resulted when persons refused to die and lingered beyond their appointed time. In the broad sense of suicide being the willful ending of one's life, then Aragorn committed suicide when he accepted the Gift. But Tolkien doesn't present this in a negative light, rather as something natural and expected. Although Arwen is upset by it, Aragorn isn't; there is no element of despair on his part. But his lying down and dying is as deliberate an act as Nienor jumping off the cliff. Tolkien, I think, had a clear personal sense of a natural order of life and death, and despair and excessive pride goes against that order, perverting it.