Because they are pretenders.
I can't really put it any other way than that. I can't come up with any logical, reasoned explanation. But the bottom line is this: with or without Paul Pierce, this team is a pretender. They'll show you some exciting play, but when it comes down to it they can't go all the way - whether in one particular game, or a post-season as a whole.
That's a cop-out. The C's have several tangible weaknesses that can be blamed before going all abstract and labeling them pretenders (what does that even mean?).
The C's have a nasty combination of weaknesses on offense. They are a terrible offensive rebounding team, which puts a ton of pressure on them to shoot high %s, only they don't have a reliable go-to scorer, which puts the onus on their sets to consistently generate good looks and/or their defense to generate transition opportunities.
Their offensive sets produce post-ups for KG/Sheed/Baby/Perk, shooting/playmaking opportunities for Ray off of screens, elbow isos for Pierce, and plenty of open jumpers for Sheed and Rondo. Unfortunately all of our big men are very inconsistent post players, Ray struggles when forced into the playmaking role, Pierce tends to rely too heavily on the inconsistent step-back and Rondo and Sheed rarely hit their open jumpers.
Is it any wonder that when the game slows down and we try to execute against an established D we struggle mightily?