Your Rx should be fine. What you need is more power for your servo load. I am going to guess that you are using the BEC integrated with the ESC to power your system? Depending on the BEC rating and input battery voltage you can over draw, (shuts down system power for a second), overheat, (shuts down system power for a while), or just burn out the BEC completely .
What you need is an external switching BEC.
I use these for my cheap foamies...
UBEC @ Amazon
These are a switching BEC's so the input voltage does not change the system amp draw rating. You do not have to use these particular ones, I just am giving you an example. I have had good luck with these, but as for all cheap electronics there are no guarantees. I guess it's a good thing they sell them in pairs.
If you have any other questions feel free to ask.