Closed loop servos are more reliable because the controller is monitoring position feedback at all times. Indeed it must do so, because the nature of a servo control loop is that deviation of the current position from the commanded position creates an error signal which goes to the drive and forces the motor to attempt to keep moving until there is no more error in the position.
I'm not sure what to think about the problem with the delayed cutting. Most likely, even with servos, the control may shut the motor down if it has too much of a following error. If the servo motor stalls, the drive amp should trip out to protect the motor. The position is never lost, but if you are quick on the feedrate override, you can slow the machine to give it more time to cut. Worst case, you would return to a known earlier position in the program and cut the same path again.
I have used AMC drives, but that is just one of many companies.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)