I think Apple has diagnosed the problem and has decided that the solution is to replace the RAM. Here's why I think so.
As I reported in this thread, I visited the Apple Store in Zurich seeking a solution to the problem described in the title of this thread (but not to some of the other problems some people are experiencing who have posted on this thread), i.e., when the MBP is connected to an external monitor running in extended desktop mode, it is only a matter of time before the MBP hangs and both displays are each filled with a single color. The genius looked at the extent of this thread and decided to escalate the case without even attempting to solve the problem. He said he would call me if he received a solution. Up until then I had thought that the problem only occurred with non-DisplayPort monitors. After my visit I acquired an Apple 24" LED Cinema Display. When I connected it to the MBP 13" the combination ran about one day before the problem occurred. So I contacted the Apple Store and was informed that Apple had indeed suggested a remedy, replace the RAM, and I should bring the machine in.
Last Wednesday (i.e., one week ago) I brought the MBP 13" back to the store and the RAM was replaced. Since then the MBP 13" has been connected to a Dell FPW 2405 using the Apple Mini DisplayPort-to-DVI adapter. (Not only the first monitor that I connected to the MBP 13", a Samsung 19" TFT, and the Apple 24" LED Cinema Display had experienced the problem, but also the Dell.) Well, the problem has not occurred ... yet. So the problem seems to be associated with the RAM, and replacing it solves the problem, at least, if whatever is wrong with the original RAM is not also wrong with the replacement. Since I am not an electronics engineer and speculation is forbidden in this forum, I leave it to others to say exactly how this might be. But one thing is not speculation: the NVIDIA graphics processor in the MBP 13" shares 256MB of the main memory, as do the on-board Intel graphics processors in the MBP 15" and the MBP 17".
For those who are having trouble convincing their geniuses to escalate the problem, refer to the repair numbers of my first and second visits, R37582360 and R37982006. These numbers might enable your genius to tap into the "communications and emailing with engineering" (quoted from the Diagnosis section of the second repair form) which evidently took place between my visits. Good luck!