I think because he's about 40 years old and has been fighting crime for a decade. I believe when Bane shows up, Bruce is already physically frail, and somewhat rusty because I do think he's stopped being the Bat for a short period of time. If he were forced into retirement, simply because Bane defeated him and broke him, I don't think he would be hesitant to come back. I don't think he'd be asking Gordon "What if he doesn't exist anymore?"
I just don't feel this version of Bruce Wayne would contemplate quitting based on his inability to beat Bane in hand to hand combat, I think it's deeper than that. I feel as though he's made Gotham better, indirectly, while Dent's influence made the public believe & the authorities more inspired, allowing him to rest, and mentally, address some of the issues he's been facing since his parents death. I think he reconciles this inner turmoil before Bane starts wrecking havoc, which is why he questions the validity of continuing this mission. I believe Bruce feels Batman may not "exist anymore," because after he comes face to face with his inner demons, that rage and pain that drove him for a decade won't exist anymore.
Actually I think this will be similar to BB, where TDK himself doesn't show up for a good length of time, maybe even half the movie. And ultimately he may decide to return, not because of a personal challenge to defeat Bane, but because Gotham falls into chaos from the truth of Dent, & finally needs & deserves a hero like "The Batman"