When you are flying your drone very fast, and then suddently let off the power, are you damaging the drone's motors? Should you instead let off the power gradually so that there is less stress on the motors? I have always been reluctant to let off the power abruptly when I am flying 35mph. Is my reluctance justified?

Cant say Ive ever had a problem with doing this over the years.

Hi there. Thanks for reaching out. It is not recommended to stop the motors mid-flight as it may result in a crash. The motors should only be stopped mid-flight in an emergency, such as if a collision has occurred, or if the aircraft is out of control and is ascending or descending very quickly, rolling in the air, or if a motor has stalled. And regarding the control sticks being suddenly released during high-speed flight, generally, the effect is not large, but if it is in the shooting process, it may affect the fluency of the video. We hope this helps.

I've done this many times with all my DJI drones and never had to replace any motors.  

It's not something I've ever worried about, and it's never been an issue for me, with any of the five DJI drones I've owned.