In my quest to attain sheer rationality and objectivity I had to overcome my own biases, prejudices and subjectivity. In doing so, I concluded that there is no rational basis for choosing life over death.
Why then, should one, when facing the meaninglessness of life, not commit suicide?
I don't think anyone can answer this question for someone else. To ask the obvious, are you currently considering suicide? Do you want help? Do you know where you can get help? If you were bleeding, you would go to a hospital for treatment. Please if you are actively considering suicide, consider many people have experienced this and found medication, counseling and treatment very helpful.
If you are not considering suicide, this is a question only you can answer for yourself. I know I have many reasons to live which have nothing to do with contemplating the meaning of life. Because I want to is a good enough answer for me.
"Why then, should one, when facing the meaninglessness of life, not commit suicide?"
Life is the meaning of life.
Don't care enough about life and can't be bothered about the consequences of your actions?
Then kill yourself: no once can force you to do something you don't want to do.
Also, sheer rationality and objectivity is impossible by virtue of being human, so good luck with that one.