I disagree with Walfet. It's the combo of a high power servo, an ESC that can't provide it and Spektrum's minimum voltage requirements.
The rx doesn't provide any power to anything, that's the ESC's job. It simply uses it, like the servo. The +&- pins in most rx's are bridged. Think of it as an internal y-connector.
When power demand is higher than the ESC can provide, voltage drops. It's this drop that causes the brownout (the rx "reboots"). I use a 1258 with a BH120 and an SR300. I use a cap because of the power requirements of the Savox servo. I had 3 brownouts before the cap, none after. It's not the end-all, be-all, but it works for me.