Game doesn't display as being open, nor does it show I'm online
The game I had open was Pokemon Sun, but after the status updated (It was showing 3DS menu previously) it shows I'm no longer online despite playing a game. I don't know if this affects any other games, but so far of the few games I've tried this is the only one that's doesn't show as working.
This is a known problem, Pokemon games turn off the console's wifi, so there really isn't anything we can do about it.
I'm unsure if this is doable in later games, but in Pokemon X/Y at least there is a workaround of sorts:
Tab to the PSS and go to the grey 'app menu' button. Open up PSS Settings on the last page, you should now see an option "Disable PSS Communications"
The PSS will now say "Disabling PSS Communications and enabling the Nintendo 3DS system's communication features", you should now get picked up and appear online/playing a game. You can tab over to Super Training or Pokemon Amie if you like. Seems to persist on future game launches.
Since online functionality has been shut down for the 3DS, I'm not sure that anything is lost with this method.