It sounds like a BEC issue....(BEC current is comming from the ESC)
The digital servo is drawing more power than an analog.
But, if you lost TH control, the issue is from the Rx out.
My first guess would be the Spektrum Rx going into Failsafe when the voltage dropped down.
The servo can also go into failsafe with low power.
Have you tried the CAP fix that Spektrum is putting out?