Here's the specs for the servo you listed http://www.savoxusa.com/ProductDetai...Show=TechSpecs.
If you look at the stall current (at locked) at 6.0 volts you'll see 3200mA which equals 3.2 amps. If you look at the stall for 4.8 volts it's 2700mA = 2.7 amps. The MMP has a default BEC setting of 5.5 volts so unless you've changed the BEC voltage it should be fine without an external BEC.

You could still have a bad servo or just got unlucky and the ESC died.