Andy writes;
If it uses a plastic tray that drops the ice by twisting the tray, and the unit is 3-4 years old or more, it MIGHT be that sediment buildup in the tray has made the surfaces rough and when the tray twists, all of the ice doesn't fall out. The next time it is filled, the water sent is too much since some of the slots are still filled, and the water bridges over the top of the tray and freezes. Then, almost none of the ice will drop out when the tray twists. Then, the water runs across the top of the tray and just drips into the ice bin and freezes.....
If this is your problem, just replace the ice tray. It snaps out and back in, and costs about 10 bucks....
I've had a Kenmore for about 20 years, and have done this every
3-4 years, and it always has fixed it......And, yess, I have taken apart the icemaker and messed with it, and I am an engineer and know about stuff ..... after doing it the first time, I don't bother --- I just replace the ice tray....
Sears has a website that you can order it in the mail.... Takes about a week.....
I hope this is your problem, as it is something you can handle yourself and save a bunch of bucks...
Andy