A lot of people have reported that, at higher altitudes, their cigars seem to lose flavor. They also report that it’s more difficult to keep a cigar lit while high in the mountains. The reason for this is the same reason as to why your ears pop when moving higher in elevation. There is less air pressure, and therefore, less oxygen.
The answer, then, quite reasonably, is yes, altitude has a lot to do with the flavor of a cigar!
Bear in mind that there’s more oxygen at sea level than at 5,000 feet, and far much less the higher one goes. At 10,000 feet, it’s sometimes hard to keep a cigarette lit, much less a cigar. And, since one has to puff harder to get the smoke, the flavor definitely take a dive at high altitudes. The less oxygen there is in the air, the more likely the flame will go out. And, the flavor is affected by the lack of oxygen. The cigar seems to taste drier, as if it hadn’t been in a humidifier.
At as little as a thousand feet, one can notice a slight difference in the taste of a cigar. At very high elevations, say, around 8,000 feet or more, one has to really drag on a cigar to get any flavor from it, and the cigar has a tendency to not stay lit. Many people have reported having to re-light cigars several times even as low as 5,000 feet. Some people have remedied this by taking only cheap cigars into the mountains with them, and saving the really good ones for the lowlands. This sounds a bit extreme.
The best measure is simply, leave the cigars at home while traveling in the mountains, as altitude really does affect the cigar experience.