I assume the chatter about Giuliani making another run is merely that. If it isn’t, let me say, as perhaps Rudy’s firmest supporter on this site last time around, that this is a terrible idea which will be rewarded by swift failure.
Political figures are not static; every episode adds to their resumes. Giuliani’s campaign in the last cycle showed that he is unsuited for national politics, hence for national leadership. His race was feckless, disorganized, and cowardly. (For cowardice, cf. ducking the Iowa caucuses. Is Iowa full of social conservatives? Well, they are Republicans — and Americans — too. Show them why you are the best man despite your disagreements. And if you finish second or third or fourth, keep going and show why you are the best man anyway.)
He had a reason to run as a leader in a time of crisis. If he is thinking of running again as a “moderate” voice, that is an even dumber idea than turning Bristol into a pole dancer.
One hears various rumors explaining Giuliani’s poor performance last time, but the meta-explanation may be that he only had it in him to do what he did for eight years in New York, plus the coda of 9/11. Nothing can diminish those achievements — although another run would further smudge them.