Some thing to ponder. Had you been relighting the cigar repeatedly or perhaps have set it down for a while and then relit it? If so sometimes the tar builds up towards the end especially if relighting.

One suggestion is by the time you get to a third left every twice in a while instead of pulling in (as if you are inhaling) softly blow outward (as if you are exhaling) - this will clear the built up smoke from previous drags and cool the cigar slightly as the heat will exist the tip.