I have fixed this exact problem before.
The speed lever linkage has a spring which stretches from the inside of the housing to the bottom of the Control Board (CB) . This pulls on the bottom of the CB keeping it pressed against the piece which pushed it out as the speed is increased (thus returning it back again as the speed is reduced and/or turned off).
The problem comes in when the spring pull overcomes the stops (notches) which hold the speed slider in place at each setting. There is a screw which can only be found when the motor housing is opened and which holds the speed lever linkage in place. If this (internal) screw is loose, the slider will not properly engage the stops and the spring pulls it out of the off position. If this screw is still tight and the slider still does not engage the stops properly, then the slider needs a slight bend to encourage it to engage the stops with a bit more force.
The Service Manual shows the whole assemble and can be downloaded from:
http://www.kitchenaidparts.eu/documents/pdf/service-manual/classic-svc-manual-new-email-version.pdf