My kenmore did the same thing, It had a duel water solenoid on it and one that let water into the door water dispenser went bad. also my ice cube started to get smaller, the rubber in the other side of the water solenoid was dry rotting and eventually ruined the ice maker. I replaced the duel solenoid and ice maker and had no more problems.The solenoid is on the back of the fridge, it is what the main water supply connects to.