This is a late generation Maytag Neptune, which most people believe is possessed by evil spirits. Actually what we believe is that the initial Neptune was possessed and the evil presence has inhabited later versionsdespite all efforts to eradicate it. I am not making this up! (well sorta)

In your case the intermittenent nature of the problem makes it almost impossible to diagnose. I would replace the inertial unbalance switch as it is a possible cause and is not expensive and its defects could cause your problem. Here is the part.

Part number: AP4027729