Well if you are exceeding the distance you should address it by bringing the system back to standards, sorry. It could be a good idea to get your cables re-tested for standards compliance. Cheap cables will cause PoE to fail at shorter distance, I have seen this before.
If you can place a temporary switch close to the AP and feed power from it that where I'd start. Also AP should report the reason of the last restart - check messages related to power ('AP reset due to Power' or something of that kind in the error log of the WLC). Sorry I cannot think of any other magic here.