I've been toying around with the 3DS for the past 5 days trying to figure out what is causing this black screen error that many of us keep experiencing. After spending countless hours on this problem, the main cause of it seems to be the Wi-Fi. I've encountered the problem in quite a few games including: Super Monkey Ball 3D, Rayman 3D, Pilotwings Resort, and even Ghost Recon, although Super Monkey Ball 3D seems to bring it on more often than any of the others.
I recently took my 3DS, my wife's 3DS, and one of my niece's 3DS systems and I ran some tests. I put Super Monkey Ball 3D in all three systems and began a wide range of tests.
Leaving the games on the title screen, where they will run demos from various levels in the game before returning to the title screen and repeat, I began encountering the error about every 20-30 minutes or so on all three systems. I then tried formatting the SD cards in all three using the FAT32 file format, which some had suggested might help, but once again all three systems incurred the errors.
I finally decided to try to turn off the Wi-Fi function by sliding the slider on the right side of the system and leave it off and then run the Super Monkey Ball 3D demos again and so far not one system has produced the black screen error and it's now been almost 3 hours.
So while there could be other causes, this seems to be the main culprit and should be able to be easily fixed with a software update. If anyone who has been having these errors would please try turning off your Wi-Fi and see if that resolved the error, please post in this topic and let us all know. 
EDIT: Just turned the wi-fi back on and sure enough, 13 minutes later Super Monkey Ball 3D gave me the black screen error. So it must be the wi-fi causing the problems. FIX IT NINTENDO! 

I hope Nintendo does get a fix out soon though. No need to tempt fate....