That fails to explain those who attempt suicide more than once.
EDIT: I found an informal estimate from this article (http://slatestarcodex.com/2013/04/25/in-defense-of-psych-tre...) by psychiatrist Scott Alexander:
"It is somewhat harder to find good studies on what percent attempt suicide again. By eyeballing some other statistics and trying to fit them together, I believe it is greater than 25% but less than 50%. One textbook whose studies I have not been able to verify says that 30% of untreated and 15% of treated suicide attempters try again."