So AA units work a bit differently than you might expect. To put it as simple as possible: Every AA unit has a certain area around itself. If a flightpath of a plane goes through this area, the AA unit will fire at the plane as soon as the plane gets spawned to the map - AA fire ignores normal range restrictions. However if the plane's flightpath does not cross the area of AA unit, the AA ignores the plane completely.
If you look at the picture below, then planes flying on the flightpaths 1/2/3 will get attacked by the AA unit. Planes on the flightpaths 4/5 will be ignored.
It is generally a very bad idea to send planes on such a flightpath that goes through base sectors - these sectors are usually protected by at least 2 AA emplacements, moreover the base sectors are often so close to each other that your AA emplacement covers part of base of your team mate and vice versa so when a plane flies in the direction of one base, it can get under fire of 3 or more AA guns and thus get killed very fast. For this reason the AA emplacements that defend your base from the start of the game have about 50% less effectiveness against planes than the versions that can be later build anywhere on the map, however even with this nerf the base sectors are still often "no-go" zones for planes.
Note that bigger maps are more dangerous for planes - the plane needs to fly longer to get to the strike area and thus if the AAs target the plane they have more time to shoot it down.
I hope this short article helped you understand the mechanics behind AA and thus will allow you to send your planes in safer directions or build your AA units in positions where they better cover the area you need.
EDIT:
I decided to add some more info on AA units in the game. There are AA units that have "Static AA mode" (M16, Ostwind, Wirblewind, WM armored car, Moebelwagen) - in this mode they dig in and stop targeting ground units and only shoot at planes.
When any weapon fires at any target it goes in this sequence: fire shot/burst -> cooldown (delay between shots/bursts) -> fire shot/burst -> cooldown -> (repeats until magazine is empty) -> reload (on some weapons has reload animation - takes longer than "cooldown")
The problem is that if a weapon fires a burst (and I think all AAs do except for 88s) it fires until the target dies/runs out of range but DOES NOT reload after. So if the gun fired at a group of soldiers and in the clip remained 2 rounds, when the plane comes, it finishes the burst (2 shots) and starts cooldown (which gives the plane time to get closer without being shot at). If you are very unlucky the unit will start reloading after the shots which will give the plane even more time to get close.
However when a unit is in static AA mode, it fires only at planes so the chance that the plane will come when the weapon has only "half burst left" is lower. It can of course happen that the AA will fire half of a burst, destroys plane and when another plane comes it will finish the burst first but in general AAs in static mode have better chance to shoot down planes even if just because of this. For Ost/Wirblewind the AA can be used only if they have the HE rounds active so these two have in AA mode higher damage against planes than in mobile mode.
Also the units reload their weapons when the enter/exit static AA mode so you can use that to your advantage too.
Generally speaking Terror and TH docs have poor AA abilities and their most destructive toys are very vulnerable to airstrikes. If you see your team mate built a KT or JP/JT and you know your opponents has RAF and/or AB, try to provide them with some AA units that will protect them from the air threats.
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