My 2003 Kenmore cold spot model # 106.50522102 keeps turning off. If you jiggle the temperature knobs it cuts back on. The light remains on.

NOTE: This
is a multi-solution answer since I don't have all the tech from your question to pinpoint your problem
But the solution is in here generically, if you read and study the solutions very,very carefully.

Sounds like the cold control has stuck . Unplug the two wires from the cold control and plug them together. Turn one wire over and plug it into the other. away from the cold control.
The cold control is the knob in the ref that turns it on and off and has numbers on it. (Thermostat)
If it runs then that cold control (Thernostat) is the problem.
If that doesn't work DO THIS:
The relay on the compressor may need replaced
A relay starts the compressor with a higher voltage and then quickly kicks out
Thats what is happening with yours
Its best for a tech to replace The relay but you can do it
Take your model number to your Local Appliance parts store they will have a diagram
showing you how to install the relay. Its called a hard start relay
also try hooking the two wires together on the cold control to route around the cold control.
Be sure the BACK COVER is in place and hasnt been accidently removed.

If you need more help GO HERE:

http://www.applianceaid.com/procedures.html

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