Probably it needs a video signal to stay on: The "Camera" input is the only one where the TV recognizes that the socket is in use & switches to that input automatically, as a convenience feature. So maybe it UN-switches automatically too?
Yes, you can select Camera from the remote (after adding it to the list), but that doesn't necessarily mean the switching logic isn't still working in the background! As usual, a B&O manual is vague: "To watch your camera pictures, connect the camera to the AV5 socket(s) and switch the television on. The television automatically registers the signal and you can see the still pictures or video clips on the screen." What does "registers the signal" really mean? No surprise if video but not audio is the gating factor, since you might be plugging in a digital still camera not a video camera with sound.