It's been my experience, whether dealing with an everyday cigar or a very nice expensive $10 plus cigar, that relighting is not a good practice. Now there is a difference between relighting the cigar that is gone out during conversation and a cigar that has been out for more than an hour or 2. I definitely do not recommend lighting a cigar that has been out for more than an hour. It's very hard to get the most out of a cigar that's been out for more than an hour. The flavors turn sour because of all the ash that's there in your cigar. The cigar ends up having a burnt harshness to it in conjunction with the moisture generated that basically contaminates the rest of the tobacco that would be good.
I've had cigars that were over $10 that upon relight were not near as good as when it was burning from the original light. If you feel like you must relight after a cigar has been out for a while, here are some tips before relighting it.
-Clear off ALL the white ash that's on the end. If you can, use your cutter to completely clip the end off the cigar, about a 1/4 inch off.
-Burn the cigar end with plenty of fire. Torch it well.
-Start puffing. Get a good burn as though it was the first light.
All this will help to recapture the flavors your treasure. While you probably won't be tasting the full greatness of your cigar, you can still enjoy about 80% of its glory.