Well if you look at those teams, they all had either one or two things in common.
1. major changes in ownership/FO
2. aging cornerstone players of the franchise that no longer produced at previous levels
Miami, Pitt and Dallas (Landry) had age and didnt replenish the roster.
Rams (Charlie Armey left the FO), Dallas (JJ) left, 49ers (Eddie D decided to play riverboat gambler, Browns (Brown got dumped) and Packers (VL split).
As for the Raiders, ownership got senile.
For the Pats, I agree, as long as BB and the Krafts continue to work as a team, manage the cap and replenish the roster (including Brady when he starts to slip), they should continue to compete for championships.