It is appropriate to ascertain their cognitive status and to try to help them delay the decision if they appear seriously impaired (due to drugs/alcohol, head injury or traumatic emotional upset).
People that are suicidal usually are suffering from something that clouds their judgement. That is why drunk people cannot consent to sex, because the alcohol clouds their judgement.
Does this depend on the circumstances surrounding their decision? What if they're dying and want to end their life in a painless fashion instead of continuing to suffer?
but excluding the fact they are high drunk or any similar situations(even tho it IS possible one can use that to prevent itself to chicken out when drunk)
Suicidal people often just need help to overcome great emotional stress. Preventing a suicide always increases the changes that life might get better. Dead is dead.
But people have been shown to consistently underestimate how much they are going to change in the future.
The decision is being made for a person that is technically different from the current one. Deciding to kill someone who is not 100% you is by definition murder, not suicide.
sources:
This 2013 study.
http://sciencemag.org/content/339/6115/96
Edit: how am I appealing belief? I mentioned a scientific study and made a simple connection. Am I assuming the science is widely believed yet unproven?