I think it will survive, just not in the form that most people think of here.
Who here knew that the NeoGeo still recieved a few new games in the 2001-2004 time frame? That's when the last game was released for the system. I'm not talking homebrew, either.
So that systems technically lasted 14 years (it was released in 1990) with new releases, if that's our technical definition of "lifespan," but I doubt that's what many of us have in mind. Look at the PS2; eight years into its lifespan, and significant releases for it have dried up considerably. It's still selling well, it's still got games coming out, but looking just two years ago, every major game being released on consoles was on the PS2, with practically no exception. Now, I can't think of any major titles that will be multi-million sellers, save multi-plats such as Madden and Guitar Hero. Nothing original or exclusive.
So, yes. I expect a couple if not all of the 3 current-gen systems will still be receiving games in 7 years. I also expect that support to be profoundly less appealing than it is now, with few exclusives or major releases from the top development teams. That's alive, in a way. They'll still be selling, and in the market. But if the suggestion is that the PS3 (or 360 or Wii or whatever) will still be at the top of its game with no replacement in the works or on the near horizon, you're fooling yourself.