You say the Mandarin, but the fly in that ointment is Ra's al Ghul can't lose a fight to the death because Ra's al Ghul can't die, not really. So even if the Mandarin bested Ra's al Ghul, it would only be winning a battle, not the war, because an enemy that can't die and that won't give up, which Ra's al Ghul won't, never loses the war. So, even if Ra's al Ghul can't defeat the Mandarin, the Mandarin will ultimately face having to make one of two bleak choices by taking on Ra's al Ghoul: either, one, fight Ra's al Ghul forever and ever and ever or, two, give up. If the first, if he's really willing to committing to an eternity of fighting Ra's al Ghul, that's not only insanely foolish but also insanely risky, because even if the Mandarin is stronger than Ra's al Ghul, all it would take is one mistake, a single misstep, and Ra's al Ghul would seize that moment to end him as forever's a long time to not ever make a mistake. If the second, isn't it better for the Mandarin to give up now and save himself all that futility, especially since it so risks his life?
Basically, since winning a fight to the death against Ra's al Ghul is impossible, the Mandarin's only chance at a win is to not fight him in the first place. Otherwise, he's looking at eventually dying by Ra's al Ghul's hand or fighting him for the rest of time, both of which sound like losing to me.