The culprit is probably the water level pressure switch
It has tubing which runs to the bottom of the tub
As water rises in the tube it increases the air pressure in the tube and this activates the switch. Your switch is not activating.
Possible causes:
Switch is shot
Tubing blocked with crud somewhere
Tubing cracked or not making a good seal at the switch allowing air to escape
Could also be the water inlet valves staying open, manually activate the level pressure switch if the water stops then it is the level switch | 
Too much water 
