It's possible that Flight 93 was shot down. It's reasonable to suspect that its target was the Three Mile Island nuke plant in Pennsylvania, not the US Capitol as reported. read more
To me, the answer to the question is “The planes were not shot down because they were not intercepted.” Had the planes been intercepted by fighters, the protocol would be that an effort would be made to communicate with the airliner by radio, by hand signals, and by wing-wagging. read more
By the time the second plane hit, they were grounding all aircraft and this one plane was not responding to orders. They didn't have time to shoot anything down. This was a rather quick timeline of attacks in a short time span. The level of these attacks was unheard of in history. It has been suggested by some that flight 93 was shot down. read more