I was gonna say - sounds like a typical 3-step mechanical speed controller problem, but obviously it isn't. Is it a Tamiya electronic speed controller? I've no experience with the Tamiya ESC's but maybe someone will have heard of this problem and be able to help.
The only thing I can think is maybe the voltage is dropping when you hammer the throttle and that's shutting down the ESC? I think I had similar experience with my Tamiya ESC in the tamtech-gear buggies - when the cells were fairly low (but not flat) on charge, the ESC would jump the car forward and cut out.
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