Motorola Droid Turbo :: Screen Dims But Doesn't Go Completely Off

I found that after my phone has been on for a period of time (hours or a day maybe) my screen will dim but not go completely dark. That is, normally it dims after about 20 seconds, then goes off a few seconds after that - like it seems it should. But after some hours of use it will dim after a prescribed time period but never go dark unless I tap the power button. If I shut down the phone and start it up it seems to work properly again for a period of time before it starts exhibiting the same behavior.