I don't see it as his spirit died in the sense that happened with Adam. Rather, that he disengaged it, put it in neutral, as it were, otherwise, satan could never have had control over him. I see it as his choice to do that--and when he tells Pilate, essentially, don't think you have any control over this, he is telling Pilate this would never happen in a million years unless he (his Father) allowed it. Poor Pilate was trying to think of any way he could to release him.
10Then saith Pilate unto him, Speakest thou not unto me? knowest thou not that I have power to crucify thee, and have power to release thee?
11Jesus answered, Thou couldest have no power at all against me, except it were given thee from above: therefore he that delivered me unto thee hath the greater sin.
12And from thenceforth Pilate sought to release him: but the Jews cried out, saying, If thou let this man go, thou art not Caesar's friend: whosoever maketh himself a king speaketh against Caesar.