Furthermore, touring was becoming dangerous. Lennon's comments about the Beatles being "more popular than Jesus" prompted massive protests in the American South, as did their performance in Japan's sacred Nippon Budokan Hall, followed by a disastrous tour in the Philipines. Quoting George, also from The Beatles Anthology: "They used us an an excuse to go mad - the world did - and then blamed it on us. And we were just in the middle of it, in a car or a hotel room. We couldn't really do much. We couldn't go out, we couldn't do anything. ... It felt dangerous because everybody was out of hand and out of line - even the cops were out of line. They were all just caught up in the mania. It was like they were in this big movie. We were the ones trapped in the middle of it while everyone else was going mad. We were actually the sanest people in the whole thing."
Additionally, the band's recording sophistication developed to the point where tracks like “I'm Only Sleeping” off Revolver were too technically complicated to attempt to reproduce live on stage. The strange sounds used in that song are a guitar solo played backwards. In the studio backwards guitar playing is very easy to do (you simply record your guitar, then play the tape in reverse), but how do you perform a guitar backwards in a live performance? Quite simply, it cannot be done.
Lastly, by 1966, all four band members were quite comfortable financially. That lack of monetary need no doubt also contributed to the decision to stop touring.
Thus, the combination of (1) touring no longer being enjoyable - and sometimes even dangerous, (2) a deteriorating level of performance quality, (3) an increased level of studio sophistication, and (4) the lack of financial need all greatly contributed to the Beatles decision to stop playing live shows. Following the conclusion of their August 1966 American tour, then, the Beatles retreated to the recording studio to begin the album that would ultimately become Sgt. Pepper's Lonely Hearts Club Band.
Beatles. The Beatles Anthology. DVD. Apple Corps Limited, 2003.