I usualy don't even reply to any problems when someone is using a TB*********x controller as they 
are know to be problematic. I am making an exception here.
 Your problem is accleration and understand  that it s directly related to your complete system 
and how they are all interelated. Also understand that the demands for doing 3d work as compared to 
doing 2D work is is greater. Based on what you have posted here is what you need to do.
1. Create a new xml file, maybe call it TESTING
2. Set the drives for 1/8 microstepping. So find the new value for the steps per unit for each axis.
    You can use the axis calibration of Mach to find the steps per unit instead of calculating them.
    The resolution for an axis is 1/ steps per unit     in theory but prsacticaly may be less. 
     Your drives have automatic idle current reduction and if there is an option to not use it don't use it.
     Don't know a recomended value for pulse width for that drive, consult you manual.
     - turn off  backlash comp
      
3. Tune EACH axis this way:
    - start with low velocity setting say 10 and double the velocity until the motor skips.  Then reduce the 
       max velocity found when it skipped to a value 30%  to 40% less. Suggest setting start accleration
      value of 1 for a max velocity value of 10 to 100, and increase the accel as you test ie; accel 2 for max value  of 
      of 100 - 500, 3 for value of 500 to 1000. ( 1000mm/min = 39.4 inches per min )
 
      After you find where the motor skipped  and have the max velocity set, do similar for the accel
      but the increase value, may be small increases ie; like 0.5 . Do this until the axis skips.
      
      Note the following:
      -You want a the highest velocity and acceleration for your system which is accurate and reliable.
        You need head room on the settings to allow for machining forces, axis change in forces to move 
         the axis, etc. Reliability is more important than speed and high acceleration is desirable.
       - a motor spec would help as that gives basic ball park info for motor tuning and just how much power 
         motor can deliver, but, yo would still do the above tuning
        - Mach3 is not your problem. 
         
         - The problem in 3D is the motor must have the ability to accel and decell the axis for small moves.
            You can have no problems doing 2D work, but the motors may be inadequate  for 3D work.
             Minimize the torque to just move the axis ( refinement of the machines axis components), 
             and provide appropriate gcode for YOUR machine.
          - steppers can skip and you would not know it but will see the affects when doing 3Dwork.
             The loss of position can be repeatable or random, usualy random so you get into a guessing
             game of what is wrong.
          - Backlash when applied properly works quite well but has no place adn can be problematic. 
            
          - as Gerry replied that the driver test may be adequate, franlky, i would comment that the 
            HZ value is probably  floating more or dropping even lower when your actualy running a
            program.
            
4. After you have configuration correct for YOUR machine. Test for skipping. Use a short length 
    gcode file form CAM. Make sure the code generated  is appropriate for your machines capabilites.
Please don't reply back (to me) and give another "guess" or even question other parts of the system until you have 
done the above.
RICH