Have you tried re-binding the radio to receiver, and recalibrate the esc, how about a spektrum capacitor
So when this happens are you going straight as with spektrum if it loses signal it would go straight ahead, depending on what the fail safe is, but you could check that, hold the car off the ground and shut off the radio while the car is on, how old is the battery and does it do it right away after a full charge??
Looking to help you out.

Reading it again, do you have another battery pack to try, sounds almost like it's going into voltage cut off