If I recall correctly, a majority of people who have 'failed' suicide (for lack of a better term) have stated that they immediately regretted attempting once it hits the point of no return.
This is just an assumption, but I think the will to live greatly outweighs the desire to take your own life. Of course their are outliers (I'm thinking of Samurai Suicides performed in front of audiences) but I don't know if there's any resources that talk about their mental health.
If anyone as any counter points I'd love to hear them - but for the most part I think suicide stems from mental instability or an otherwise inevitable physical death (terminal illness, old age, etc).
One other reason it may be linked with mental health, is the fact that if mental illness is not a factor - what is driving these decisions? I can't imagine that people come to the logical 'master of my own existence' that you mention.
It's a very interesting subject, when you take the horror an tragedy out of it. Also curious what other species have high suicide rates, or if its a primarily human affliction (don't have time to dig around on this right now).