There are a few pieces of evidence that suggest long-term depression can impact neurogenesis, which could lead to altered cognition. I don't know if that's a prevalent theory, and as the author points out, it doesn't explain non-depressive suicides.
I can, however, answer this anecdote with another anecdote. I've been dealing with suicidal thoughts for about 5 years, and at some points some very limited self-harm. On an earlier post, I detailed what I thought was my most frightening, closest-to-suicide moment.
> The scariest, closest to suicide moment I ever experienced was when I was shopping at a mall. It wasn't very busy, and I was feeling very... manic might be the word. Head down, headphones in, speed walking between errands. I had to keep moving, no matter what. I noticed the sort-of cut-away in the floor, so you could see from the top floor down to the ground. It was only 3 stories, but I had a really strong, sudden impulse to vault over the railing and see what it would do to me. Maybe I could land on my head, that might work. It was something I had never really considered before, it wasn't a very efficient way to do things, but it just gripped me very suddenly and all of a sudden it was a huge crisis.
Being suicidal, generally, is death by a thousand cuts. You have a predisposition, and all the stresses in life push you in that direction (as you've said). But the jumping off the ledge moment is crucial; personally, I have strategies for daily temptations like putting away knives in the kitchen. It's the spur of something unexpected, the sudden, strong, irrational impulse that really scares me.