Melee has been around for 12 years. No other game has ever had such sustained activity for this long a period of time. And, remarkably, the community is arguably at its strongest; so far removed from the game's release.
Instead of questioning whether Melee will die any time soon, you ought to question the longevity of its competitors. Just because they're newer doesn't mean they'll last longer. How long do you think Injustice will last? Is Street Fighter IV going to live through the inevitable V? What will Brawl be like in 5 years?
Melee's community has an extremely strong grassroots scene behind it. Corporate (MLG, EVO, etc) support goes in and out, but the grassroots will always be there. The core tournament organizers of the Smash scene are all Melee vets. When Smash 4 comes out, it will be hosted in tournaments run by Melee vets. As Project M gets better, its inclusion is entirely at the discretion of Melee vets. etc. Now tell me, what are the chances those organizers are just going to let Melee die, and stop including it alongside those other smash games? We're talking about the Juggleguys, Team OXYs, D1s, SilentWolfs, etc of the world. Do you think any of those guys, who are the actual hosts of all these tournaments, are just going to stop promoting Melee? Even if the newer games catch fire in popularity?
I can give you a list of reasons, but that ought to be enough. 2014 is going to be incredible for Melee, so you're coming in at a wonderful time. Just go to tournaments and have fun.
The funny thing is, the issue you're citing is what most members like about Melee the most: there is no deadline for improvement. We all just assume Melee is going to be around forever. Unlike other games (say, a new Mortal Kombat comes out...you have to get good before its first EVO because its doubtful it'd be back for a second one), its easy to keep Melee as a hobby and improve gradually, because, realistically, it isn't going anywhere. Ask around, and you'll find more smashers think Melee will be around for another 12 years, than not.