Maybe that is the reason. Maybe the fans anxiety (at the game and in general) feeds back to the players and affects their performance.
Picture the scene, Saints winning comfortably a splendid 2-0 lead and around the 65th minute the opposition take advantage of a miscue and suddenly it is 2-1, what is the general behaviour of the fans in the ground? Nervous? Muttering, "uh oh, here we go again.."?
It is not inconcievable that the anxiety of the fans affects the players, fans of other more successful teams probably don't get as anxious as they have seen their team bounce back so often, but with Saints, a 1 goal lead and 5 minutes to play, i've lost buckets of sweat and bit my nails until they were bleeding at Saints matches...