I don’t know whether there is evidence of atheists being at greater risk for suicide in the population at large, but this article http://www.allvoices.com/contributed-news/15156588-atheism-is-a-suicide-risk-us-marine-corp-training-document-claims suggests that there is such evidence in the military. One possible reason for increased risk, if it exists, is obvious: if life is painful and death is nothingness, death may seem preferable. Religious people might be dissuaded from suicide not just out of fear of hell, but out of a general belief that the universe is basically good and things will be better in this life and in an afterlife, and that belief can sometimes sustain a person through terrible trials.
Thinking about this issue strengthens my conviction that there need to be religions or things like religions that atheists can use to get (if I am right about this) that same sense that the universe is basically good. This doesn’t need to be based on some unsupportable belief that the universe cares about human happiness in one way or another. For me, I am able to maintain my sense that life is good and getting better by doing things that I have learned will support that sense. I don’t mean to suggest that other atheists should do what I do, but we all need ways to maintain our hope and happiness in the face of the suffering that life will inevitably throw in our path.