I've just run into the same display port problem with a single monitor, where the windows reposition themselves when the monitor is power cycled, as though it is using a different resolution.
Dell U2410 monitor
ATI FirePro V4900 card
Win 7 x64 box
I tried installing the monitor driver, and adjusting the USB power setting suggested above, but no luck. I've switched to the DVI port and the problem goes away. I can't figure out how to get into the EDID settings within CCC to try out the other suggestions in this thread. Thanks to everyone who contributed their experiences, I was very glad to see that others have had this problem too.
The V4900 has a single DVI port and 2 DP ports, I am hoping if a 2nd screen is added, using a DP to DVI adapter will avoid this. It is weird that there is no real fix for this, it seems like a major bug.