Well, you made a statement which is very helpful, you said
"We do not have an analogue aerial plugged in"
Whilst you do not have an aerial plugged in, have you tried pressing the TV button when the fault occurs instead of Sky using DTV ?
The one thing which still points to a AVANT power supply problem is the statement you made where you said the AVANT screen does not have a raster at all, so to be sure, next time it fails press the MENU button on the Beo4 and if you do not get the menu on the left hand side of the screen the setup menu, it is almost sure to be a power supply fault in the AVANT.
Are you really sure there is no blank raster when you have the problem, remember you can only just see a blank raster when correctly setup without a signal ?