That's a silly argument. You're saying because it's a scatter gun and you can't really tell who's at risk you should fund the extra money to women more.
but since men have 4 times the successes they are still a better investment even if you can't target at-risk people.
I'm actually saying women are the safer investment for targeted funding because it's easier to get a successful hit on a suicidal person that way, even if that person was not going to die from their suicidal efforts. Any expenditure that goes to a non-suicidal person is essentially wasted resources in the short term, and there are costs, social, financial and physical involved in attempted suicide even when it doesn't result in death, so preventing an attempt that wouldn't have been fatal is still a gain, while spending effort on someone who was not at risk provides little to no gain.
The thing is if there's more widespread harm caused by the non-lethal effects of 3 attempted suicides than by 1 successful one, to simplify the ratios, which is actually quite possible considering the effects suicide attempts can have on those around a person, then women are the better option, if the 1 death is more detrimental to society than the 3 attempts then men are the better option to target.
Granted even in the scenario that the cumulative disruption of 3 attempted suicides outweighs that of one successful one you still have dead people from the successes, which is tragic and lamentable, but the value of societal wellbeing vs individual wellbeing is probably a bit beyond discussion here.
EDIT: To phrase the above the clearly, there are secondary effects to suicide, successful and attempted, in addition to the simple death or survival of the suicidal person themselves. What's actually more efficient an expenditure of money depends on how damaging you consider these effects compared to the death itself and how severe they are in the smaller number of successful suicides compared to the larger number of failed suicides./EDIT
In regards to palsch's post above, my brother and I both struggle with clinical depression and suicidal thoughts, him more than me, and have done so since our mid-teens. Neither of us have sought professional help beyond medication prescribed by our GP, and I would primarily attribute it to the general idea that we're supposed to be stoic and in control of our emotions. His response to depressive moods and suicidal thoughts is to shuffle into a dark room and spend a while avoiding people until he's suppressed things again, mine is to get angry at myself and things around me until I've quashed them for a time.
There's no good reason we don't get proper help. There's plenty of support available, it's even entirely covered by the NHS here and supposed to be very effective according to some of our friends who've needed counselling and therapy for the same reasons over the years. We're just culturally conditioned not to seek help. Personally I blame it on stoic manly man media from when we were kids, the whole only babies and girls cry thing and the general idea that men don't talk about their feelings, hard to shake that crap off.