I have read all the posts on this subject. I have exactly the same problem - the random G that makes the 8720 go offline. I must then unplug the printer, replug and it will work perfectly until the next random G. I have gone through all the suggestions given and none make a difference. Since several people have posted about this same problem it seems as though HP needs to take a serious look at what will fix it. I don't want the hassle of taking the printer in (we all know it is a BIG machine) and then maybe getting it fixed while I am without a printer I need to use full-time. Sure I can keep unplugging then plugging - in spite of bumping my head every time I crawl under the desk. I am sure for every person who posts about this problem, 10-fold more have the problem. So I suggest HP needs to take a hard look at this problem.
The printer is brilliant otherwise but this really is a big annoyance.