I'll tell you what happened because it happened to me and my wife at an Anime Con, Your GF streetpassed the 3DS before yours did and she happened to be number 10 filling up their 3DS and leaving you unable to receive theirs until they clear theirs out. If they weren't checking theirs then there would be no way for you to receive them as well which sucks but hey what can you do.
So what exactly are the limitations? You can only have 10 street passes sitting outside the plaza at anytime? And once you greet them in, you must use them all before sleeping 3ds again or else you can't use them in find mii? Any limits on how many you can have INSIDE the plaza?
Just putting the 3DS to sleep doesn't do anything. If you keep the application open and get a StreetPass while it's running, there will be an arrow icon that allows you to bring in the next group of Miis. If you use the arrow before using all the Miis you've currently collected you'll lose use of them in the games, but it's fine to use it afterwards. You'll also lose them if you bring them in to the plaza and then don't use them before midnight (but if you haven't brought them in you can keep them indefinitely). And if you quit the program and then restart it, the next group will be brought in automatically, unless you haven't used all the ones you have yet, in which case it will warn you and give you the chance to use them first.