When sick periods happen, they seem to fall mostly between 6 and 18 months of age, in my experience. However, not all cigars go through a sick period, again, in my experience. One of the worst I have personally experienced was a box of BBF's that started tasting bad right at 7 months. I have never had any PSD4's go through a sick period and that is the stick that arguably has the most complaints. I believe a lot of things come into play here; the crop, the treatment of the tobacco prior to rolling, humidity, storage conditions, the factory and probably a host of others. I have had some sick cigars that are disgusting, including RASS, Bolivar Coronas and the BBF's. All are devine when they get past that stage.
I have noticed that a number of people on this board have also commented about "down" periods for very old cigars. It would seem that cigars go through highs and lows over the years, including those with a few to many years of age.