Couchcowboy,
The operative fact here is that, while this fix seemed to work--did work--for a day or two, the problem soon returned. Or maybe it never really left, but something that I did while doing all the things the Apple rep told me to do helped, but then stopped helping.
Whatever. I am no closer to having a solution to this problem than I was before. I have a workaround, of course. I've set the iMac (with the latest OS X) so that it is never put to sleep automatically. I put it to sleep by hand at the end of the day. I can deal with resetting the connection once a day.
Most of the time in the morning, I should add, the internet connection is still there, but *sometimes* it isn't. I find that very puzzling. There seems to be nothing going on at night, when it's asleep, so how could there be a difference in the morning?
Just as a side note, I have a Logitech Squeezebox internet radio. When the iMac loses its internet connection, the radio doesn't work at all. I guess it needs to get some information or other from the Logitech web site. Perhaps the presets are stored there. That's just annoying, when I get up in the morning and try to listen to the radio before I check the computer. Maybe I'm the last one left who does it that order, but I often do.
Anyway, I'm sorry that I raised false hopes. But it was the Apple support person who got me to clean out that PRAM. Shouldn't they know better? Another support person that I talked to wanted me to reinstall my OS. Do you have any thoughts on the probability that this would help?
Steve