An update on my situation. I am using the 2011 Macbook Pro with an NEC 2490WUXi display, but have also now tried it with a 17-inch and 19-inch Dell monitor, both 1280x1024 resolution.
No problems whatsoever with these relatively small, five to six-year-old Dell monitors. But with the big NEC display (1920x1200) the problems continue.
So far, the workaround is to disable the power management on the NEC display (the NEC display is timed to sleep much faster than the Dells), physically turn the display off each time you're not using it. And each time I turn it on, I also have to do the following. First, switch on the monitor and open the lid of the computer (trying to bring it up in clamshell after switching the monitor off, then on, results in two displays rendering all-black). Then, once both displays are up and running, leaving the monitor on, close the lid of the computer. Then, bring it up in clamshell.
Overall performance is slightly better on average — but not consistent or predictable — with a Dual Link adapter cable. But at least the performance on the standard DVI adapter is consistent and predictable. I've given up on the Dual Link for the time being because every now and then there's a big problem.
Note that this is all with a 15-inch Macbook Pro. This computer EXCLUSIVELY uses the AMD Radeon chip for external displays. I have been checking configurations closely and at no point does the computer resort to the integrated graphics for external support, and disabling integrated graphics in the control panel does not alter this flaky behavior. People who discuss this issue on the thread should note which MBP they're using, especially if it's a 13-inch Macbook Pro 2011, which depends on Intel's integrated graphics, or an earlier 13-inch, which has a discrete chip using integrated memory.
What I see here is a faulty driver that can't handle autosensing by monitors, aggravated by the somewhat low voltage that comes out of a DisplayPort. I would like to see Apple fix the driver and NEC offer a firmware update that would allow more user control over autosensing and sleep. I notice reading through this thread very similar problems with a 24-inch Dell display, but at least on that it looks like the person was able to disable autosensing, which isn't an option, it would seem, on the NEC.
A logic board replacement or computer replacement will not solve this problem. Been there, done that.