Every war since Vietnam the US has enjoyed air superiority and the enemy has developed tactics to counter.
In Vietnam the massive amount of logistic support allowed the VC and NVA to use a lot of anti-aircraft machine guns.
In Afghanistan mujahadeen fighters would pack 51 caliber machine guns up mountain tops to shoot DOWN at Soviet HIND gunships.
In Desert Storm an AC-130 "Spectre" was shot down by an Iraqi Strela-2 manpad missile.
In Serbia CPT Scott O'Grady was shot down by an SA-6 missile that used a civilian air control radar for initial guidance.
In Chechnya terrorists would tape shrapnel to RPG-7 warheads and set the fuse for time. The warheads would go into the air and create a shotgun blast of shrapnel.
In Mogadishu plain RPG-7 warheads were shot into the air, and enough hit to cause "Blackhawk Down" to become history and a movie.
In OIF insurgents would identify Air Mobility Corridors and set up a triangular ambush with machine guns. With fire from three sides it would overwhelm the pilots ability to react and evade.
Now here is the kicker, every successful air defense used by the underdogs requires some sort of advantage in outside support (Vietnam, Serbia) or massive amounts of munitions (Chechnya, Mogadishu), or good intelligence (Afghanistan, OIF). And in only one case was a "high flyer" taken out (Serbia).
So if you want to take out the high flyers you had better do it on the ground. This is difficult because air bases are usually far from where the fighting is and are generally well protected. Al Quaeda in Iraq (AQI) was able to mass several hundred fighters to attempt "liberating" Abu Ghraib for propaganda reasons, but totally missed out on trying to create a point of penetration on an air base. Of course the failure of the VC/NVA to capture any air bases during the Tet offensive might have led them to believe that it was futile, although communist sappers did destroy several aircraft on the ground during the war.