Hi
i had some problems also with POE injector or switch, i used some HP pro curve
HP 2915-8g poe switch and i used to have the same problem because HP didn't respect the poe spec,
Now i used cisco poe switch and no more problems,
You can try to start you AP with the ac adapter (and the poe cable insered )and when the ap is running unplugged the ac cord, i try this on a setup and it work.