That actually is a very good question. I think that many GOOD bands fade because they lose their edge. GREAT bands, on the other hand, are essentially timeless because of their musicianship and (in many cases) raw instrumental energy. One guy that pops into my head is Dave Grohl...I think that he's one of those guys that will be rocking well into his 70s.
We can even start to throw Green Day themselves into this category. Have you read the May edition of Rolling Stone? The cover story is largely about Billie Joe Armstrong, and what I read surprised me. The dude is basically a suburbanite who coaches his sons' Little League teams (true story, and a great mental image if you think of him coaching in his punk garb), and yet he still has a very deep, dark reservoir of emotion and passion for music from which to draw.
Armstrong, Dirnt, and Tre are all 37 now, which might not quite be "past their prime", but it's still impressive to see them churning out good music a couple decades after they started as angsty teens.