It depends on your definition of [i]last[/i]. Will people still be playing Destiny in a year? Yes, I can guarantee it. Will people continue to buy the expansions? Yes, I can guarantee it.
As for how many people, who knows? I can only assume the numbers will drop off over time, like with any other game out there. Personally, I'll stick around as long as I'm still having fun. I might bounce back and forth between games like the Witcher 3 and the new Battlefield, but having clan friends here on Destiny means I'll always have something to come back to.
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To the point where it's more cost effective to shut it down