First off, if you don't have the time to smoke a full cigar down to your fingers, don't smoke one. This is one of the main reasons why cigar companies make different sizes. If you have only 30 to 45 min to smoke a cigar, stick with a Robusto, but if you have a couple of hours to kill, a Presidente might be in order. However, if you just have to cut that Churchill short, there are a couple of techniques that won't have you lighting up a real stinker when you relight your cigar.
When a cigar goes out, there is no more air or smoke moving through the cigar, which means that the smoke and tar that is already in there will settle and "flavor" the tobacco with an undesirable taste. If I know I'm going to put out a cigar to smoke it later, I gently blow out of the cigar so that I get all the stale smoke out of the cigar before I let it extinguish. This results in a cigar that, while not at pre-light quality, will relight easier and without the nasty taste that you sometimes get when you relight a cigar. Also, there are cigar tubes that extinguish the cigar by depriving it of air. Just put the cigar in the tube while lit, close the cap, and the cigar will automatically extinguish. The case also makes a great storage and transportation container.