I think it could be caused by ATI powerplay and a problem with the driver and 2D clock settings at non stock 3D clocks.
When one display monitor is connected on the 5800 series and the card is in 2D mode the card is downclocked to 157Mhz core and 300Mhz memory.
When 3 displays are connected the 2D clocks are raised to 400Mhz core and 1000 Mhz memory.
If the default 3D clocks are changed in MSI afterburner or ATI overdrive to anything other than the cards default 3D clocks the 2D clocks no longer get set to 400 and 1000 with 3 displays but go down to 157 core 300 Mem.
Most of the black screens with displayport happen for me at times when the GPU could be adjusting clocks like when watching videos, starting games, surfing websites with flash content etc.
Creating profiles with MSI afterburner and making sure one of them is default clocks so the correct 2D clock settings are used in 2D mode can help.
This doesn't completely cure the problem for me but does reduce it. I think a complete cure could be forcing 2D clocks and 3D clocks to be the same so the card doesnt change states.
Stock 5850 3D clocks sets 400 core 1000 Mem 2D
Non stock 3D clocks sets 157 core 300 Mem 2D
