The wire arm when it is raised up and locked will shut the ice maker off. When it's in the down position a lever will strike and close the on/off switch so that the ice maker is on. The wire arm is pulled down by a small spring. Each time the ice maker starts to harvest the wire arm will slowly rise up so that the ice dumps out under it and then the arm slowly comes back down. If there is enough ice in the bucket to stop the arm from coming all the way down to close the on/off switch the ice maker will be turned off. Once the ice is used and the ice level drops the arm should drop down position so that the ice maker will be on. You should feel the spring tension as you raise and lower the arm. You should also be able to hear a faint click of the on/off switch when the arm is at the lowest point. Sometimes the lever that strikes the on/off switch will need a little tweaking.
You can view a parts diagram of the ice maker at Sears.com and click on Parts. Enter your model number and click on ICE MAKER under the Sub Components. The lever that strikes and closes the on/off switch is key number 24. The part of the lever that strikes the on/off switch can be straightened out just a little so that it will close the on/off switch each time the wire arm comes down.
The ice maker will need to be removed from the freezer in order to make this adjustment.