Many times but not always, this boils down to the linkage "elbow" need to be lubed. Not too tough of a fix. Remove the wiper arms, then the plastic air vent grills, then look at the linkage.. You will see that there is a short linkage at the motor that connects to the main linkage to the wiper pivots. Where this connects is the "elbow". It is a "cammed" linkage. when the motor rotates one direction the cam is in one postiton and when the motor is shut off, the motor rotates the opposite direction causing the cammed elbow to change position causing the wipers too "park".
Sorry if you are totally confused. Suffice it to say if you get the gist of the elbow, and you lube it with light grease/heavy oil your problem will go away.
Regular motor oil is a good choice. Grease gets too thick in winter to allow the cam to change position.