Sounds like it could be the BEC in the ESC glitching. The answer to that is either send it in for repair, buy an external BEC which you route from the battery directly to the RX bipassing the ESC (be sure to disconnect the red wire on the ESC so the RX doesn't get 2 different voltage inputs), or buy a new RX. Like you said, sounds like the RX is okay if it runs fine with battery and two servos(as long as one of them is the same servo you seem to have troubles with).

What type of servo is it?