Appeal to reason is probably not the best strategy, suicide being the result of a mind surrounded in a storm of negative emotions. Not a neurologist or mental health professional, but from first hand experience I can tell:
* You may not commit suicide here and now because it is a one-way ticket to Hell, and an insult to God. So you are trained form childhood to suppress those thoughts at all cost.
* You may not commit suicide here and now because you fear that a loved one will find your corpse.
* You may also not commit suicide here and now for fear that your attempt will fail and you will end up crippled and your life will suck even more (and you may loose your ability to commit suicide latter).
* You may not commit suicide here and now because some people that is supposed to help you out completely drops the ball, so you get so pissed off that you break out of your melancholy out of sheer anger (this happened to me once, when I reached out to a church-operated emergency hot-line and nobody picked the damned phone).
Of course, you may always opt to do it later. But the point is that it all revolves around emotions, so any counter has to have a strong emotional component (either direct, or through the underlying neurochemical substrate).