This sounds like the inlet water valve assembly may have trash/sand/debris inside allowing water to leak by... Or the springs inside the solenoids may be deteriorating enough to let water seep by but that's typical of older valves than yours... This assembly can be removed and taken apart for inspection/cleaning or you can replace it (AP3040319) altogether... Turn off the water supply before removal and be sure to inspect/clean the inlet screen as well... I recommend a water filter be installed in the water line before the inlet water valve even tho your model has one inside the fridge compartment... cheers, kooler