I solved the problem by running powercfg -hibernate off
from an administrator command prompt, and then rebooting.
[Credit to cncb
on the Green Button forum for suggesting this]
I suspect my previous Vista setup may have had hibernate turned off already, but installing Windows 8 reinstated it. If that is the case, then probably the remote control power button always hibernates if that is enabled, and only sleeps if it is not.
Of course, life would be even better if you could power the machine on from the hibernate state using the remote button, and scheduler could also auto-start the machine from hibernate for recordings - then a small amount of power would be saved. But I am happy for it to be working as it is.