Mixer turns on revs to a high speed and then quits

How long before it restarts again? I'd take the back cover off and have a look around and test for continuity in the relevant places when stopped and unplugged.

Try replacing the phase board, it's above the speed control plate with 4 wires coming out of it.

Replace the phase board, that's the small pcb under the back cover with 6 wires coming out of it.

Sometimes can be caused by running too fast on the lower speeds. Should be 13 to 15 revolutions in 15 seconds on speed 1 then a slight increase only on speed 2.

You can get the high speed back if you want to play with those three screws. there is a timing scheme for your mixer and it is set and adjusted by manipulating those 3 screws. The bottom center screw is for speeds 6 8 and 10. The best choice is to replace this switch, about $10 bucks on ebay.

Obtain a copy of the Repair Part List for your model from Kitchenaid.com.
Download a Copy of the Kitchenaid Service manual.

http://www.kitchenaidparts.be/centers/servicemanual/mixer.pdf

First, you may want to adjust the mixer's speeds:

1. Loosen the lock nuts enough & Turn the 2 top screws clockwise until they cannot be turned
anymore. Leave the bottom screw alone for now.
2. Use a dab of white paint or paper whiteout to mark the positions of the Phillips screws.
3. Plug in your mixer and Set the speed selector to "Stir".
4. Turn each top screw One full turn couterclockwise (alternating between Left and Right)
Keep making one full turn at the time (for both left and right) until the motor starts running.
5. Put your hand near the Agitator shaft and allow it to brush your finger slightly. Use your
watch or clock and start counting the number of times the shaft touches your finger in
60 seconds. The correct count should be 60 RPM (Rounds Per Minute). If it is less
or more than 60, give each screw 1/4 turn counterclockwise or clockwise and start counting
again. Now tighten both lock nuts.
6. Set the speed selector to "6" and turn the bottom screw either clockwise or counterclockwise
to achieve a speed of 180 RPM.

For your reference, the planetary RPM's for the 5-qt. tilt-head Artisan Stand Mixer are as follows:
Stir speed - 60
Speed 2 - 95
Speed 4 - 135
Speed 6 - 180
Speed 8 - 225
Speed 10 - 280

Second, if the mixer won't run:
Remove the Control Plate Assembly (36), the Phase Control Board (39)
and the motor Governor Assembly (35). Inspect for loose connections,
burnt or damaged components. If they seem to look OK, re-assemble
them and test the mixer. If the motor still won't run, then I might suspect
a defective Phase Control Board (39).

your control plate is worn out. it will need replacement.

By not working to mean that the planetary gear wont move? or does it just make a weird noise when it is on a low setting? If the gear is completely stripped the unit shouldn't run on any speed regardless if there is mixture in the bowl or not. Since I can't see the mixer I would say that there might be a slight tear in the gear which would only allow the mixer to get stuck on a slow speed where as on a high speed it is running fast enough to skip that particular tooth. I understand that the mixer is brand new but when it comes to mixers you can strip a gear right out of the box depending on the consistency of the batter you are mixing. If the machine is under a year old it is under warranty and you are allowed free service by an authorized repair center in your area.

I'm not quite sure about this answer but it occurs to me that it could be the governor. It sits at the back end of the armature and as the speed control is slid to faster speeds the governor moves away from its rest position pressing against the control plate. If the governor's pivots were to be binding, even slightly, it would explain the symptoms you are describing. A service manual can be found at:

http://www.kitchenaidparts.eu/documents/pdf/service-manual/classic-svc-manual-new-email-version.pdf

your kitchen aid has a little device inside called the hall effect sensor. These often come dislodged or just stop functioning. If you are mechanically inclined you can replace this yourself.