Takemaru: You don't know when to give up. Inuyasha: I just don't like giving up. There's a difference.
~ Inuyasha showing his determination against Setsuna no Takemaru
Determinators are characters who make their pledge to never give up...ever, no matter what. There is no stopping the Determinator. They do not understand tact. They do not know when to fold them, and it's a waste of time to tell them the odds. No one can reason with them. They'll do whatever they have to without question. For this type of hero, no price is too great to pay for success, up to and including their own life (and others). The audience doesn't expect them to realize they might be better off letting it go, even if they can barely stand. If their allies or families are ever kidnapped or lost with no hope of rescue, they'll be the one who will find them, and they will stop at nothing to do so. Their adversaries will even shout, in exasperated rage, "Why won't you die?!". For them, there is no line between "perseverance" and "insanity."