I think the whole '1 puff a minute' thing is overthinking things entirely. I've known guys that love to smoke their sticks napalm hot: I used to smoke with a guy who would literally do 2 to my 1. I'm quite a slow smoker by comparison, and I don't care if I have to apply a fresh match to an almost extinguished cigar because of it.

Sounds to me like you have a stick with a crappy burn. Happens to us all, and I generally just forget about it and move on...