I had a BEC/servo issue with 2 planes:
1) Cheap digital servo failed and caused the BEC to overheat and shutdown after a few min. The giveaway? The ESC kept beeping every few min indicating # of cells, presumably every time it reboot. That's when I found the heatsink was very hot.
2) Damaged a HXT500/SG50 servo by plugging it in backwards. Flipped the connector around to the correct polarity and the BEC would overheat within a few min and shutdown. It actually got so bad, the voltage regulators on the ESC melted the heatshrink wrapping!