I am surprised no one mentioned this but I think you have a seperate issue from humidity, or storage or how fast or slow you are smoking. I think you are lighting you cigar the hollywood way. In the movies, you see guy taking a a flame directly to a the foot and they regin puffing. BIG FLAMES... LOOK LIKE BIG MAN. Survey says? eeeeehhh
If you are drawing in heavily to get the cigar lit you are drawing flame right down the middle. You need to take the lighting process a bit more slowly. When using a torch, you can hold the flame 1/2 inch away and watxch the tobacco toast or char evenly. then as it get hot, your cigar will look like this.
at this point the cigar can be smoked and you never had to puff while lighting it.
if you are using a BIC or other soft flame, be sure the edges/wrapper are lit or charred before puffing on it. This way you are starting off on a even burn and not begining with flame right down the middle.