What is the meaning behind dark works often taking place at midnight? A recurring story element that I've noticed is the accessibility of certain evil/dark devices at midnight.

A few examples:


In the third episode of Sailor Moon, girls listen to a midnight radio show that is hosted by the antagonists illegally. Girls that wrote into the show and are read on air receive a brooch which steals their energy. 
In Persona, there is a midnight channel which broadcasts the shadow of the person that is currently missing.
In Jigoku Shoujo, there is a website that is only accessible at midnight, which will allow the user with a grudge to send someone to hell. 


Why do all three of these anime use midnight as a time for evil? What is special about midnight that sets it apart from any other time?
This is an example of pathetic fallacy, more specifically an empathic environment. i.e. giving an environment a percieved emotion. It is a common literary technique.

Some other examples include:


Rainy scenes when a character dies / delves into depression.
A calm breeze after turmoil has subsided.
A big storm buffets the castle walls as the evil king rages
The sun appears from the clouds as the characters see a new path to follow after being downtrodden
It snows and the land is harsh when a man is exiled from the city. 


In this case, midnight - is commonly associated with spookiness, feelings of unease and the supernatural. 

It also conjures images of darkness, which is commonly associated with evil - where light is usually a good force.