Nolan's trilogy makes it very clear in the beginning that there are two threats:
Internal threat = organized crime (Maroni & Falconi families)
External threat = League of Shadows
For all Bruce knew the LoS was dismantled after Ra's died. And in the time between BB and TDK he and Gordon focus on the mob bosses. After TDK Dent's legacy allows Gotham PD to take care of the mob as well as lower-level criminals. So, in the couple years after TDK both the internal and external threats are taken care of.
Therefore, there was no need for Batman in the time between TDK and TDKR. The way I always imagined it was in the couple of years after TDK, Bruce still followed criminal activity and maybe hacked into GPD servers. He saw that crime was going down and Batman taking the fall for Dent was more or less serving the purpose Bruce meant it to serve. Naturally Bruce was able to focus more on the fusion reactor as he was less worried about crime...until Pavel's paper and so on.
Anyway, the point is that Nolan's Bat Universe doesn't have this endless rogue's gallery that the world can constantly throw at Bruce to perpetually force him into being Batman. At the end of TDK Bruce decides that his job as Batman has pretty much served its purpose. Hell, he decided the same thing in the middle of TDK, but nobody had a problem with that.
Comic Bruce doesn't retire because DC has to keep telling stories and making money. That's really all it is. People can keep pointing to the comics and saying, "Bruce would never quit," but that's only because the show must go on.
The groundwork is laid in BB for Batman being a temporary
pursuit. TDK further explores Bruce's contemplation of moving past the cowl. TDKR deals with the aftermath - the emptiness Bruce feels as a result of all the things that have transpired.
BB = Fear
TDK = Chaos
TDKR = Pain
God I love this trilogy. It saddens me that hardcore Batfans didn't like how it ended. I'm not trying to be rude, but for reasons explained above I just think a lot of people couldn't set aside the more improbable fantasies of the comics and appreciate the story Nolan told. A good friend of mine even admitted so. He said he just couldn't be rational about things he didn't like in TDKR because of his emotional attachment to certain aspects of the comics. I love Batman just as much as anyone. I haven't read anywhere near the amount of source material others have, but I'm a lifelong B:TAS and Beyond fan.
That said, I was always able to view Nolan's trilogy as a certain interpretation of Batman. A little more grounded and cerebral. Quite frankly Nolan took the best aspects of Batman and put them into the best live action depiction the character will ever see for a long time. In a strange way it reminds me of Jackson's LOTR and how he took the most interesting aspects of those books and made those movies. Both directors got to the heart of what matters most in each set of stories. For Batman it was always Bruce's personal journey in dealing with his anger and grief. I don't mean that to be condescending or disapproving, but I can't fathom why people who are so invested into this character couldn't appreciate what it meant for Bruce to finally, literally climb out of a pit of hellish despair and choose a life beyond Batman. I can understand if people value the idea but didn't like aspects of the execution. Then again I feel all the reasoning and development are established in the films. But if there's one thing I would say, it is:
The real giving up would have been remaining as Batman