what voltage and amps does your BEC put out? I had a simular problem in two of my monster trucks, they both ahve the Hitec 5945 digital. In my Savage when the rx pack gets low on charge the steering servo will stop working but the thyrottle will be fine. In my TXT-1 I am running the digital up front and a standard in the rear for 4WS and under high loads it would do the same. I added a rx pack to the TXT and now it works fine until the rx pack get low on charge.
Just a thought.