The “valve”, as you call it, we call a “float” must be in the up position. This stops the water flow into the brine tank. It is connected to a valve system in the bottom of the tube in the brine tank that opens when brine is to be drawn. After all the brine is drawn out then that valve system closes by the vacuum created when all the brine is drawn out. At the end of the regeneration cycle the last thing is water pressure goes back to the brine tube to refill the brine tank. As the water is rising it will push the float to the up position until it closes the valve system. It sounds like something in that system has failed. I suggest you have a Kinetico repairman check it or another water conditioning dealer or plumber that will work on that unit check it. It usually is a minimal repair cost.