From: OH, USA
Actually, here is some evidence. 4th army had 7 heavy AA SU assigned to it for a total of 168 88 mm and 42 20 mm guns.
The image shows that three recon flights highlighted in red were intercepted by all of the 88 mm's, and then they participated in only one more battle with ~150 enemy planes. The next battle in the hex, they were probably out of ammo, and the 48 20 mm guns participated. Most of them ran out of ammo, and 24 participated in the next battle in the neighboring hex. After that, nothing besides intrinsic antiair from attached support units. Of course, this represents only about 5-10% of the German AA capability, but extrapolated, this is still quite underwhelming in terms of the in-game cost of supply transport and out-of-game micro time to set up antiair.
Panels on the right indicate that all of the ammo in the units were received this turn, implying that they ran out of ammo. Again, comments appreciated. I don't expect miracles but I also think 300+ units worth of micro and decision-making shouldn't just be shoved to obsolescence. Clearly, the same mechanics affect the soviet player as well, as they will have to spend AP to save or create AA units, although to a lesser degree because it's highly unlike germans will be able to carpet bomb as we see here.