You should be a bit more descriptive to help us diagnose:
What type of esc/brushless?
What RX/TX combo?
Turn limit for esc and motor(if brushed)?
The only thing I can think off the top of my head is a thermal shutdown scenario, where the motor draw overheats the esc and it goes into a failsafe mode. It doesnt explain the servo freakout though....
get us some more info...