Unstable A/V output after resting

My Flex has this weird issue where if it rests unused for a short while, the audio and visual outputs it displays completely butcher themselves in quality.  The video output will have a bunch of little white dots overwhere, like static, and the audio is unlistenable because of how high of a frequency that it skips.  Disconnecting and reconnecting the Flex to power makes it go away, but it seems sort of self-defeating for an always-on box like the Flex. 

I've had the TV for several years, and no other device does this.

Is there any way to resolve this issue?