A bit of a long shot but....
The fact it is intermittent and better for increasingly long periods until it is ok makes me think that maybe it's heat/expansion related? There could be a slightly loose or damaged cable/connection somewhere but as your hardware heats up the slight expansion fixes it.
One way to check would be turn off the tv, amp and Sky like you would normally do - like you're off to bed - and turn everything back on straight away. If you still get the same issue you can safely disregard my hypothesis!
It could also be early signs of impending hardware failure somewhere.
But whether it's my heat idea or something else you can try to eliminate the different devices as the cause. For example connect the sky box directly to the TV leaving the AV receiver out of the equation. If you have access to another TV try connecting that instead. If you have another source (DVD, Blu-ray or games console) use that instead of the Sky box. Hopefully that will allow you to narrow it down to one device.
