I see this happen in my car form time to time as well. My opinion was in the way the HU is wired to power. My installer wound up having to tap a line directly from the battery. As such it seems to be a drain on the battery. If I wound up not driving it for sometime I notice it is worse. When I have taken extended trips out of town it seems fine.
My sense is it is a battery drain issue, with driving it recharging the batt some, I will have to hook up a battery tender to my car this weekend to see if its simply the drain that's the issue. I also have an issue where ipod video just drops out to a blank screen. Almost as it the wired connect is lost randomly. I then have to re click the pandora or video icons to get it to come back.
I have yet to have anyone give me a resolution for this seemingly random problem.
When it disconnects I see a white square on the head unit on the left side for a split second.
I wish there was an answer but as for not powering up, check to see how you were wired for power. If its direct then maybe just a recharge to the car battery every once in awhile will fix it.