What would cause the cold water not to shut during the wash cycle?

well it would seem these are the possibilities:
1. cold water not turned on
2. hose kinked
3. inlet valves not working
4. wiring issue
5. control board issue
oh and plugged inlet fill filter
good luck

U need a technician for that... there is a problem with the "flow valve" sorry can't help u out much with that... but maybe u can visit this site and hit the like button... www.facebook.com/muktidayasewa

Clean or replace the cold water valve. you are a flood hazard.

usually the wash is a mix of hot and cold and the rinse is just cold, that said, it is most likely a problem with the cold water supply. check to make sure the cold water valve is all the way open and the hose isn't kinked. If those are ok turn the water supply off and remove the supply lines on the machine side, you will see a screen inside the washer that may be clogged with sediment. If so, just clean it out and put it back together. You may also want to run a wash cycle on cold only to see if it fills slowly for the wash cycle. If it does fill slowly on cold you have low pressure on the cold side.

The timer is at fault.
During the spin cycle the timer should send intermittent power to the water valve. This activates cold to help rinse soap residue from the laundry.
If cold is continuous it means the timer is not breaking correctly.

It's overfilling If your washer is overfilling, check these:

Water-inlet valve
Water-level switch
Water-inlet valve A defect in the water-inlet valve may mean that it's no longer able to shut off completely when the electricity has been turned off to it. If this occurs, the valve may leak and drip water into the clothes tub. In time, the water may accumulate substantially. If this happens, you need to replace the valve.

Water-level switch A defect--or an obstruction--in the water-level switch may mean that it can't tell the water to shut off. So the machine overflows. This switch senses the water level in the clothes tub. It's usually a diaphragm device with a small, clear tube attached between the switch and the bottom of the washer's outer tub. As the water level in the tub increases, the pressure on the air in the tube increases. When the pressure reaches a certain level, it activates the switch, shuts off the water, and signals the timer to begin the agitate cycle. You can either clear any obstruction in the tube or replace the water-level switch.

It's underfilling The water-level switch regulates your washer's fill volume. This switch is usually a diaphragm device with a small, clear tube attached between the switch and the bottom of the washer's outer tub. As the water level in the tub increases, the pressure on the air in the tube increases. When the pressure reaches a certain level, it activates the switch, shuts off the water, and signals the timer to begin the agitate cycle. If the switch is defective, it may prematurely signal the water to shut off. If so, you probably need to replace the water-level switch.

The water temperature is incorrect The temperature of the incoming water determines the temperature of the water in your washer. You get either hot, cold, or a mix of the hot and cold water that's currently available to the machine. So if the cold water that enters the machine is very cold--or if the hot water entering the machine is very hot--the warm water is affected. 

If you live in a Northern climate, unless you adjust the hot and cold water taps that supply water to your washer, the warm water supplied to your washer is usually hotter during the summer months and colder during the winter months.

while the unit is filling in the warm cycle. reach behind and shut off the hot water tap.I bet the water flow stops filling, if so, you would need to change the inlet valve on the machine. You see, in warm, if the cold is not filling, you still hear the hot filling and the unit will advance. The rinse cycles are mostly "cold" only. if the valve is not opening it will not allow it to advance from the rinse section on the board.

Good luck!

If you are getting no water spray during the rinse cycle that would cause the soapy clothes issue.

Are you getting cold water during the wash/rinse cycles? If you have the machine set to warm/warm you may only be getting hot water while the final spin is calling for cold.

If you have cold water available then the timer is not calling for the water spray. The problem is either in the mixing valve or the timer.

it sounds like your mixture valve is faulty on the cold water side. that is the valve where you screw the hose ends on. it needs to be replaced you can purchase one at your local sears, be sure to take your make and model number with you

In the machine, you have a solenoid that the water hoses come into. That piece is controlled by a timer. The hot water during the cycle, does it shut off completely during fill or intermittent?