It seems that after going through a heck of a lot of tires (I've ridden over 26,000 miles) that, on average, the tires become much more prone to flats.
Now, I know they wear down some so maybe that small change in thickness could be a factor, but I wonder if other things are in play. Mainly, I wonder if, once you get a flat, that whatever the puncture was caused by has also damaged the tire in some way so that the next tube get a flat from rubbing on these less than perfect places in the tire.
Likewise, maybe those little cuts you accumulate in a tire does the same thing in some cases.
Those are the only reasons I can think of for increasing flats over time.