I had the same problem on my iMac 27". Apple replaced logic board, video card and display and the problem would secure after several weeks or months. Very frustrating. I eventually replaced the machine and several months afterward decided to do a "nuke and pave." I completely reformatted the hard drive and installed a new OS. I have not had the black screen problem since then. The machine has been running smooth for several weeks with high graphics usage, i.e. FCP and video encoding. I am thinking now that this is not a hardware problem but a software problem and it must be some obscure driver or bad programming with the sleep command. Perhaps permissions or corruption.