battery is more than enough. Is it a bad motor I am wondering sending spikes back down the ESC causing it to do a shutdown to protect itself. obvioulsy its under load when it goes out. Tracking I wouldnt think has anything to with this. neither does vibration. put a foam under the ESC and try again. It shouldnt make a difference.
And loading the servos makes it not brown out too... you said.. Did you hold the pressure for a long while?
Running on the desk, the motor is pulling nothing more than probably 10 A anywaz.. with the blades, even.. Thats too is a stretch
When you turn the motor , does it have grittiness or a noise?
next thing just like you did on the servos. load the motor on the bench without blades..
take off the blade grips and rotor head yoke. .leaving just the shaft. (assuming tail bladea re off) .. run the motor up, and load it on the bench by grabbing the shaft with a thick rag or something to try to load it .. thats the only thing I can think of.. and yes try the foam under your esc too .. see if that helps (shouldnt) .. if it does,,, you might be looking at a loose ESC solder or something. (remote chance) but try this