A study out of Oxford University has found that prisoners with a lot to lose upon entering prison - ones who are married and employed prior to being imprisoned - are more likely to commit suicide than unmarried prisoners who were unemployed upon entering prison.
This is the expected result if suicide is a rational decision. But, for some reason, the researchers recommend increased investment in mental health services (coercive suicide prevention) for at-risk (married, employed) prisoners. Huh? Because if someone has a good reason to commit suicide, and therefore is at higher risk for committing suicide, he must be . . . crazy.
Other results of the study include the fact that serving a life sentence also increases the risk of death by suicide, as does living in a single cell (the latter, presumably, not just because of loneliness, but because it makes committing suicide easier in practical terms).
Mental health services - generally a euphemism for coercive suicide prevention tactics and other ineffective, humiliating practices - are the wrong solution to the "problem" of rational suicide. The idea that "mental health services" are the right thing to do to reduce suicides is ubiquitous, but it's important to point out failures of rationality like this.
Update: apparently chronic pain - especially head pain and pain in multiple areas of the body - also increases the risk of suicide.