Rationality has many different definitions/meanings/usages, so that a simple answer is difficult to give here. And difficult answers I no longer have the brain capacity for unfortunately.
However, for a simple approach there is the hedonistic calculus. A method that stems in utilitarianism where one works out the sum total of the pleasure (+) and pain (-) of an act. Now, compare this value with the alternative act, and the act with the highest value is the "right" course of action.
I'd say that for the suicidal, the act of living has a negative sum total, as our lives mostly exists of pain and suffering.
I'd argue that the act of dying results in zero, as there is no sensation or feeling any longer.
Zero > [negative value], thus dying is the right act to choose.
I have two observations though:
-An utilitarist point of view should also take in account everyone involved. So your suicide might affect negatively other people, and you should put that into the equation.
-How can you feasibly measure the amount of suffering you'll have in the future, as it has yet to come
But certain mental illnesses are incurable... That's why people can request euthanasia on the basis of mental suffering in compassionate societies like Holland, Belgium & Luxembourg
Like I said, when it comes to mental illness things are not so easy. And I think it should be evaluated case by case.
I mean, some mental illnesses are incurable as you said, but in most cases they're treatable, and a lot of people will respond to treatment. Or they will find something that makes their lives worth living.
I do agree with assisted suicide, even in cases of psychiatric disorder, but there must be a judgement on whether a reasonable amount of things have been done to help that person. I mean, let's say a depressed individual says he wants to be assisted to die. He has have never ever tried even a SSRI. He has never visited a therapist. And on top of that, he has been depressed for only a year (I'm exaggerating a bit to make a point). Would you provide assisted suicide to this individual? I wouldn't.
So between this fictitious individual and a stage 4 cancer patient, there are a lot of shades of gray. So I would say, I think it should be allowed. Just not for everyone.