That sounds like any of the following:
- battery itself incapable of supplying enough power to the motor/esc -> is the battery fully charged? if yes can you check if it has a C rating (aka a discharge rate) anywhere? (batteries with higher C rating can readily supply more power on demand, since you said it only happens at higher speeds)
- what ESC is it? any sort of branding available that you can use to look up the specs of? could be a lousy ESC
- how's the wiring? (like what Mike suggested)
and not to be pedantic but it helps to be more descriptive (as in: is the problem reproducible? what sort of action was done before you experienced power loss/power cutoff/whatever it is? is steering still functional; can you still steer the front wheels when that happens? so and and so forth); we're only psychotic, not psychic