Buffy dying in Season 1 brings Kendra
Kendra dying in season 2 brings Faith
Faith = current Slayer = not dead
Of course, all that is pretty much thrown out the window with that "everyone's a Slayer" shit from Chosen.
God I hate Season 7.
But Buffy is still a slayer. They never, ever said it had to be the current slayer.
Seeing as how all past slayers have tended to...stay dead when killed they probably didn't feel the need to get so specific about it...I always figured that each slayer only passes the torch the one time when they die, which would be why a new one wasn't called when Buffy died in The Gift.