The first speed control was probably shutting down as the BEC would struggle to handle 12V and a servo. A better BEC would be about 3A or you could go to a switching BEC for higher voltages. (I am coming to this from aircraft and cars.)
Receivers and servo run on perhaps 5V. The BEC has to take the 12V of your battery and step it down to a voltage that won't fry the radio equipment. That 7V differential is disposed of in heat. If you add multiple servos, high drain servos, (and the small ones are often higher drain than we might expect), or a binding linkage, you are adding more current, creating more heat which has to be dissipated by the BEC. Usually, speed controllers can deal with up to 4 servos on 6 NiCds, (7.2V), 3 servos on 7 or 8 cells, (8.4-9.6V), 2 servos on 9 cells, and 1 servo on 10 cells. Better controllers are more tolerant of stretching these guidelines, and cheap controllers often don't.
Martin