The fact so many of these suicidal folk are atheist especially the ones who dont even have health problems should tell you all you need to know.
Perhaps you have failed to consider the reasons that have led to people becoming atheists or becoming suicidal. It could be the case that both are caused by the same things, but the reasons might also be completely different and unrelated to one another. When I first became an atheist, I was much less depressed than I was as a Christian. That changed after a while due to negative life circumstances, some that were my fault and some that were not, but those circumstances are the things that have led to me being on this site. All I can say for sure is that Christianity never gave me any hope. Once I opened up the Bible and saw the horror show inside of it, I became filled with an increasing sense of dread that only went away when I realized that the god claims in it might not even be true.
At the moment, I don't think of myself as an atheist anymore. I do believe in an intelligent creator that is responsible for the existence of the universe, but it's not enough to change my mind about suicide. Maybe if I thought it was actually a benevolent and loving creator, I would feel differently about it, but when I see the way that nature works and the absolute brutality that occurs in the animal kingdom, I see no reason to think there is a loving god, therefore, I am a theist that still wants to die. Putting aside all of the suffering that happens among humans (because a lot of it is caused by humans, even if not all of it is), the things that happen in nature are enough to make me suicidal. If a lightning strike can cause a wildfire during a drought, which then leads to wild animals being burned alive, then those very same things could happen to me, or you, or any one of us. If a god designed a universe where these things can happen, then it must either be apathetic or sadistic. Regardless of whether or not a god exists, that is not a world that I want to be a part of, therefore it seems like a valid reason to be suicidal. If you think this reason is invalid, then maybe you could explain why.
Based on your response, I would have to say that your own personal bias against non-belief has led to you assuming that atheism is the reason for people being suicidal. You also seem to not realize that some of us are suicidal because we know that physical health problems that will result in a hellish existence are inevitable (even if we don't all have them yet). These things could be something that happens suddenly and unexpectedly or things that happen slowly and get worse over time. Perhaps knowing that these things are likely is enough to cause someone to feel suicidal because they want to avoid those things happening. Maybe that is not the case for you, but it is for me. It wouldn't matter if I was an atheist or theist, I would still feel the way I do about this regardless.
Maybe it would be a good idea for you to think about the response you gave all over again and consider whether or not you might be incorrect in your conclusions. Responses like yours that don't appear to have much thought put into them, are no different than a forced lifer that has no understanding of what we are feeling, telling us that our reasons for considering suicide are invalid and using pro-life platitudes to convince us of why we are wrong.