Before you attempt this you may want to first check the latch keeper located on the tub, this is what the latch catches on. It can be adjusted to make the door close tighter and ensure the switch is activated. It is held in by a couple screws that need to be loosened and then push the latch to the rear a little, retighten screws and test. Also make sure are closing the latch tightly!

Here is a parts breakdown for your appliance that may be useful in locating parts: Model DU466-40


Could be a few things, loose, worn out latch or bad door inter-lock switch.

Click here for switch: Part Details - MAYTAG Switch, intrlck, part number: AP279015

Click here for latch: Part Details - MAYTAG LATCH, ASSEMBLY, part number: AP3970873

The inner door will have to be removed to access these parts, make sure the power is removed from the appliance!! The door switch can be tested for continuity with a meter. It should NOT have continuity (door open) when the button is up and it should HAVE continuity when you push the button (door closed). If the switch is good then inspect the latch and make sure it is working properly (hitting the switch button). Always remember how you take parts out, so you can remember how and where they go back in.