Hmm.
If you are using a single 4s lipo with the normal dual battery leads, are you also using a jumper plug connected to the un-used input? Heres how you should have it wired up:
Just pretend its a hvmaxx esc with one motor.
Otherwise, how do you have it wired up normally? I wired my old hvmaxx esc up to use a single 4s lipo back in the day, and it worked fine; I can only imagine something isnt wired correctly. If this is a newer hvmaxx pro (black heatsinks), then check the esc's LVC setting too.
Cant say it should be a BEC issue, even on 4s lipo the internal one only gets a bit warmer than normal- unless the servo you have is some un-Godly digital thing that eats up the amps?..