After playing with these solutions for a while I've come to the conclusion that it doesn't work, unfortunately.
But I also have a clearer picture of the symptoms. In the end I turned off all power savings and still have the problem of internet not being accessible after a period of inactivity (at least an hour of so). The only way of getting internet again is to restart the computer. So I think that rules out the power savings as being the culprit. Also there is the odd occasion when I start up the computer in the morning and I have to restart before accessing internet.
Another bizzare occurence is that the power saving settings keeps reverting to the default every time I turn the computer off, even though I save the new settings. On other computers we've had, similar problems were solved after finding and changing power saving settings in BIOS, and I was surprised to discover there were no such settings in this computer's BIOS.
Isn't it funny how problems can just appear and disappear out of the blue and we're all none the wiser. Maybe windows is just one complicated computer game where we are to solve problems and go on to bigger challenges, the end revard being a job with Microsponge.