First, Air Force One is not a fixed designation. Any Air Force plane that the President is on board of is given the call name Air Force One for the duration of the flight. Other typical names are Marine One for the Marine Corps Helicopter he flies in sometimes, as well as Navy One or Army One, etc.
Second, the current two Boeing 747's (Air Force designation VC-25A) that have been modified for personal use of the POTUS does have Missile Countermeasures. The publicly known countermeasures are EMP hardening, Chaffs and/or Flares, and Electronic Countermeasures, specifically IRCM.
- About five AN/ALQ-204 Matador infrared (IR) countermeasures devices are located at the tail and behind the four engines, Previously used on the VC-137C (Boeing 707-320B) presidential aircraft and on airliners and executive aircraft, the device emits pulsed IR signals to foil attacks by heat-seeking missiles.
- An AN/AAR-54(V) missile launch warning receiver located at the tail is intended to report and track missile threats by zeroing in on their ultraviolet exhaust signature. The receiver is also in use on special-operations warplanes like the MC-130H Combat Talon II.
- The AN/AAQ-24 Nemesis Directional Infra-Red Counter Measures (DIRCM) system, which can be directed by the AAR-54, fires pulsating flashes of IR energy that confuse a missile’s guidance system.
-Defense Media Networks Article
They may, and likely do, have additional countermeasures that are not publicly known, for reasons of national security, obviously. This may include air-to-air missiles or retractable laser anti-missle platforms.
But the biggest defense is fighter jets that are ready to launch within the minute if needed to protect Air Force One. Escorts are standard outside of continental US airspace.
So while the VC-25 Air Force One planes do have countermeasures, why they didn't work can be chucked up to one simple thing. No countermeasure is perfect.