Their popularity since the sixties is really not debateable as the Rolling Stones are still together and touring for over 40 years. Stones are popular but that's not what makes them one of history's international icons of rock. People just like bluesy raw rock and roll and that's probably what keeps selling their tickets.
Stones have staying power, something Britney Spears has yet to prove and do the Eagles even tour together anymore? Even if they do it's only after a few of their members had gone solo meanwhile the Stones' lineup all still remain , minus the band's founder, Brian Jones, of course.