Fairport Convention - only Simon Nichol from the original lineup, but he hasn't been there the whole time.
But it's a band that evolves with people coming and going, I don't see why a and like that shouldn't go on forever as longs as (a) there's some genuine continuity (Viz. some of the Iommi on his own 'Sabbath' albums) and (b) they keep producing new material that builds on the original corpus rather than becoming a 'tribute' to themselves.