I discovered that there were two separate power related issues that caused this problem. Hopefully this will help anyone who has a similar problem. The first problem was that the power adapter was faulty. Replacing it solved part of the problem. However, after I replaced this item the screen would request a shutdown unless I had something drawing power through the USB ports. This was dealt with by turning off the functionality of the physical buttons (this option was inaccessible until after I replaced the power adapter for some odd reason). The real solution did not occur until I changed computers. Ever since I upgraded to the new Retina Display iMac I have had no problems with this display. I can use the physical buttons and I don't need to have anything drawing power through the USB ports.