Yes, the .nds and .sav files need to go into a folder, not on the root. She didn't rename them from the archive (she just dropped them straight onto the card) which will make them difficult to identify! I also notice that some of them have .SAV instead of .sav (lowercase) as the extension. All the extentions should be lowercase, especially the save files.
Also check to make sure she has the latest firmware. And delete a few of the games to make sure the microSD card isn't nearly full.
If putting them into a folder doesn't help, the problem could be anything from a corrupt file system (which mean you'll need to reformat) to a bad microSD to a bad DSTT (not making proper contact with the microSD). Since it's loading in the OS without errors, it seems to be limited only to certain files which makes me think the filesystem is corrupt or you have a bad microSD card. Either way, I'm not sure how you're going to get around reformatting in order to track down the problem! Back up the microSD card, reformat (preferably using the Panasonic formatter), copy the firmware back onto the card, make a "games" folder, drop 2 or 3 games in the folder, and see what happens.
-Bri