A lot of people seem to have issues with the inconsistencies in the slayer line on the show, so I went through the show to try and find a reasonable explanation, and I think this pretty much covers it.
Here’s a timeline of events that fall into this theory:
PROPHECY GIRL (1x12)
Buffy dies, passing the slayer line on to Kendra; Buffy is no longer ‘The Slayer’, just a girl with slayer powers.
BECOMING PART 1 (2x21) Kendra dies, the slayer line is passed to Faith.
THE GIFT (5x22) Buffy dies, the slayer line is unaffected.
Willow calls Buffy the ‘warrior of the people’ (AKA the Slayer) in her resurrection spell. Buffy is revived as The Slayer, splitting the line in two.
SMASHED (6x09) Because Buffy is technically The Slayer again, the demonic aspect of her strength is ‘surfaced’, explaining why Spike’s chip doesn’t fire off.
SEASON 7 The slayer line splitting (Buffy’s resurrection) causes the ‘instability’ that the Bellajoxa’s Eye tells Anya and Giles about. This creates an opportunity for the First to rise.
Hopefully this helps to fill some of gaps left by the writers.