Some fridges have a safety feature built in, which turns off water if the water valve was open for a certain number of seconds, to avoid flooding. So if you need a lot of water, make sure to release water dispenser lever for a second or two every minute.
If the above is not the case, you may need to replace the water valve
or a switch
on the water dispenser.
The way to find out which part needs replacement is to check the voltage on the green water valve coil when the dispenser lever is pressed but it's not dispensing water. If 110v AC is present across the coil - replace valve. If there's no 100v AC - replace switch in the dispenser. Make sure to unplug the fridge before opening the dispenser.
VladFirst Choice Appliance