Sorry for the late reply, I had a family emergency.
Thanks Alex for your input.

I checked some stuff and these are the results:

Wye/Delta relays seem to function OK.  They are activated after the green CNC Power button is pressed and click decisively.
I also examined all eight contacts and cleaned them to make sure there are no burned spots.
 
I checked the motor windings for shorts.  No shorts.
The resistance between legs  on the motor is 0.3 Ohm for each pair of legs.

I  disconnected and took apart the resolver on the top of the motor. It is clean. Just in case I wiped the disk with the lint free cloth (the one used in cleaning fiber optic components) as well as the detector. 
I put it back together.
This did not change the machine behavior.

I also managed to run some more tests (described below) to look for some regularities.

Test 1:
I turned the machine on and set the spindle speed (in MD) to 4000 RPM.
I activated the spindle (M3)  and the motor started with some rumbling which quickly disappeared on it's way to 4000 RPM.
I increased the speed all away to 5500 RPM without any unusual noise.
The spindle was then left running for about 3 minutes.
I shut the motor down with M5 and the rumbling sound appeared right before the stop. 
The spindle stopped in about 3 seconds.

Test 2:
I turned the machine on and set the spindle speed (in MD) to 2500 RPM.
I activated the spindle (M3)  and the motor started with much more rumbling than before which again  quickly disappeared on it's way to 2500 RPM.
I started manually reducing the spindle speed slowly and the rumbling began at about 1800 RPM.
The more I decreased the speed the louder the rumbling became.
At about 1550 RPM it became unbearable.
Then as I was increasing the spindle speed gradually the rumbling gradually was disappearing until I reached almost 1900 RPM at which speed the rumbling was gone.
I repeated the same procedure without stopping the motor about a dozen of times. Every time with exactly the same results. 

Test 3:
I turned the machine on and set the spindle speed (in MD) to 150 RPM.
I activated the spindle (M3)  and the motor failed to start right away.
It kept kicking on for several times but finally started with distinct bumping sound and stayed that way on 150 RPM for about 5 minutes then the machine went into emergency stop by tripping the motor overload relay.
I think the message was Error #8.
I shut down the machine.
I reset the relay (White button see new picture 264b.jpg) and I noticed that two terminals (T1 and T2) on that relay were very hot and one (T3) barely worm. Actually the hot part was the center portion of the relay.

After these tests the spindle had difficulty to both: start and stop decisively.

I shut down the machine and after about 10 minutes I was again able to start the motor and run it at 2500 RPM. With same results as in test #2.
This time however the spindle had difficulty to start.  (See new video:  Post2.wmv)

I looked at the explanation of an Error #8. Where is the spindle magnet sensor?

I also checked all terminals inside the vector drive for loose wires and visually checked for any burned components.

The new video and some more pictures can be found at: http://www.flex-mount.com/fadal/fadal.html