I can say with confidence one of the reasons that does NOT help Mario endure today is story, and that really says it all, because Miyamoto himself has said gameplay is what he focuses on.  When the issue is framed this way, between story and gameplay, well… as long as we're talking video games, great gameplay will win over a great story every time.  I'm talking about how long Mario is in the air when he jumps (Naughty Dog commented on this once), giving Mario a cape or a tail, the ability to turn into a frog or shoot fireballs, and I've only touched the surface.  These things change with each new Mario game.  When was the last time Mario wasn't chasing after the Princess?