Get a receiver cap for it.
Some servos put alot of hash/noise back into the reciever (poor design)
This causes the receiver to reset/restart.
The receiver cap filters out the noise/hash. This is more of an issue with the cheaper/generic servos.

Have comfirmed this with my o'scope (I had a 3A BEC)
The rx's are good down to approx 3v(from memory) .

If you have a high torque/high current servo it should be powered separately if the esc's BEC cant cope. Get an external 3A or 5A BEC for it.