"What is the reason for your delay?"
Translation:Qual é a razão do seu atraso?
Prepositions are difficult. It seems like certain ones go with certain expressions. Regarding qual, a good rule of thumb is whenever you have what is or what are use Qual.
This would certainly not be "which" in English, and it carries no sense of there being a fixed set of options to choose from. How can we guess it´s "qual"? Does "razão" always take "qual", for example?
Why couldn't "Qual é a razão POR seu atraso" be acceptable? "Para" seems to indicate "finalidade."
Nothing wrong. Everyone will understand you. But it is less usual in this construction/context.
In Portuguese, you usually ask the "reason of something" (the "reason" which is "part of something").
"Qual a causa do seu atraso?" and "Qual o motivo do seu atraso?" are also more usual than "... por/pelo seu atraso".
It would not be the first choice, but you could use it.
"Crafting Peace: Strategies to Deal with Warlords in Collapsing
Sasha Lezhnev - 2006 - Political Science:
... motivate more people to stay on board in their organizations for reasons of greed."