There is a bit of a discordance here, worth exploring. As physical, breathing beings with any feelings (unless you truly have a pathological condition) you are, inherently an emotional creature. Even the most rational of rational decisions are based on your emotions, your learnings, and nature. Otherwise, if you removed all emotion or such from the equation, everyone given the same set of stimuli would make identical decisions (as it wouldn't vary or be coloured by what makes you, well, you).
It is impossible to be rational without being emotional. While emotions can overwhelm the level of perhaps one's rationality (ie, if I wasn't feeling so emotional, would I have made the same decision?) rationality cannot really exist without emotions. As that is what makes things understandable to you, in this world, as you calibrate to your own experiences and feelings ... Emotion can disrupt reasoning in certain circumstances, and yes, you can have someone whose emotions overwhelm them to the point their suicide or indeed any behaviour, is not rational.
Regarding the point of whether people with chronic disease, or mental illness, or age are these for which suicide is the only valid reasons, we'll, inherently these are subjective. Would I know if I didn't feel I had a mental illness, or was too old, or wanted to commit suicide that these were rational or irrational decisions given my circumstances? Would I assume, based on others telling me in their world view these things should, or should not, be a basis by which I am mentally fit or not to determine if suicide is appropriate for me? Nah.
Suicide is a personal decision, and a personal state one has to, in some way, shape or form (other than where completely clouded by an emotional state) come to terms with. If it is something you arrive at, believe logically makes sense (even if that is because the world makes no sense to you or not), and feels right, then to you - it is a rational decision. Just because that doesn't match up with others views does not by definition, make it that you have a mental illness (ie if the judge of mental illness is how off kilt to the conformity with societal "norms" you are, I would suggest far greater than one in five people have a mental illness - they just hide it better!).
Too long; didn't read version is yes, it can be rational. It can also be emotive. Rational is in my mind better, as you have at least thought it through, benefits, risks and consequences, and regardless of your emotive state you have made a decision. And it is decision that is important, regardless of what others see as write or wrong. It's not their lives. It's yours.