After their 2nd promotion to the Premier League in 2000, IIRC I don't think that Charlton were ever under any danger of getting relegated at all during the next 6 seasons under Curbishley. During Pulis's final season at Stoke for example, they were a couple of points ahead of the relegation zone with about 5 games left I think after they lost to Man Utd (although I never thought they could go down as there clearly more than 3 teams that were worse than them), but Charlton under Curbishley never even faced that sort of pressure from 2000-2006.
I think they tended to have a very strong 'middle third' of the season, raising fans' hopes of potentially qualifying for Europe, before fading during the final stretch and settling for a mid-table position, so some of those fans became increasingly frustrated when that script continued to play out.
Also I think there was a period when they seemed to have an exceptionally good record in London derbies.