I just got my HD 7870, but i have a problem with it, every 1 maybe 2 hours my screen gets black and gives me the message "no signal". Sometimes it comes back again, so i see the google page for a few seconds, and it dissappears again. With my former card, GTX 560, i never had the problem. It could be a monitor problem, though, because it is quite and old and damage (1080p) monitor.
its a problem with the amd drivers, i get this on my 7870 aswell, go into windows power options and just prevent the screen from going into standby if you leave the pc for an extended period just turn the monitor off.