HVAC Blower Control Cables

I have a 2011 Corolla LE, and the HVAC Blower Control Cables (55906D and 55909C) have stopped working. The ends of the wire cables have slipped off the actuators and so the knobs don't work. I can put the wire cables back on the actuators, but they just slip off again as soon as I try to manipulate the knobs.

Has this happened to anyone else? What was the fix? Is there any alternative other than replacing the cables?