조중현, "That" is the most acceptable answer due to the definition of the verb "to demand". Martin's boss is demanding why... A person can demand why. Demand means to ask with authority. Martin's boss is asking why he takes occasional three-day leave to get away from the pressures of office work. Martin's job is demanding that.... A job can demand that.... Demand means "to require" when referring to things. Martin's job requires that he takes occasional three-day leave to get away from the pressures of office work. ------- Informally, you could think of "Martin's job" as the " the people in authority where Martin works". Then you could say "Martin’s job is demanding why he takes occasional three-day leave to get away from the pressures of office work. But strictly speaking, a job cannot ask a question.

that A job doesn't demand why. Only people demand why.

"why" is correct. -If "that" is used here,there must be a noun in front of it cos the relative pronoun is used to replace for a previous noun. Examples:+He is the only friend that i know on this site. +There are many demands that the beginner have to learn well in our company. -However,"why" is the shortcut "=the reason why" to show/ask/request...the explanation/reasons. "Martin's job is demanding the reason why he takes OCCASIONAL three-day leave to get away from the pressures of office work" Other examples:+I don't know why(the reason why) the plan B is not accepted. +Can you tell me why you have the strange attitude like that?

Martin’s job is demanding ( that, why ) he takes occsinal three-day ...... Martin's job is demanding, that is why/ because of that, he takes .......... We need the reason, the why he takes a break: because his job is demanding, That is why he takes that break. It is just like that. I hope, I could help you!

That is why Use all three. It is how you will make this sentence clear and saying what you mean.