I've had this quite a lot too.
Most of my kit (BD/Vero/Squeezebox) is connected directly to a Denon amp and then to the TV via a single HDMI. The 5000T is direct to the TV on it's own HDMI socket with audio from the TV via optical out to the AMP. The first time of the day when I switch on any piece of kit then the 5000T will also switch on. This can be by a remote or by pressing the hardware power switch.
I have the 5000T switch on overnight for 30 mins as recommended to grab the EPG and so this is the the first time after that happens. I wonder whether the shutdown after that is somehow different to a user shutdown because the 5000T does not switch on if using any other kit later in the day - it is only ever the first time I switch on in the day.
I do not have any kind of CEC enabled on any device since it's more trouble than it's worth and I have a Logitech remote to do everything I need.
Hope this gives some more clues for what is definitely a 'problem' albeit one I can live with
Thanks
-Mat