I'd ask for Hundredmillion's help here, since he's so much better versed in Lacanian psychoanalysis. But I would say in watered down sublayterms that male suicide has to do with ego--men/male sexuality is much more built up around the male ego, so when things go wrong, there is more at stake. A man's individual worth is made up of his place in the community, his professional accomplishments, his belongings, his property. Women don't traditionally own property (we have a patrilineal system of property inheritence in agrarian societies), don't have a "value" outside of the domestic realm. As a woman, you aren't allowed to feel like your individual ego is worth anything to the point where there's no ego to be devastated by setbacks. (You just get to despair in silence and unfulfillment because you don't matter anyway, that sort of thing...) If a woman loses her job, even her high-powered career, it's usually not her entire sense of identity/sexual value.
Rates of suicide are higher for men, but many would guess that rates of depression/mental illness are only less diagnosed in women (not less common) because they're less likely to result in violent outcomes when untreated. In fact, they've found that women who live under the veil in Middle Eastern countries suffer from ASTRONOMICALLY high rates of clinical depression.
Here's another question: if men are less "emotional" than women, why are they responsible for nearly all "crimes of passion" as defined in common law?